** Whole the work is done manually on excel sheets**.

Below are **bimagic squares** written in blocks multiples of orders 8 and 16. Most of the work is done manually by author in 2011. Few of them are with the help of **Aale de Winkel** <aaledewinkel@magichypercubes.com>, Magic Encyclopedia magic square, magic cube, magic tesseract, magic hypercube. See the reference below:

**Inder J. Taneja**, Bimagic Squares of Bimagic Squares and an Open Problem, Febuarary 11, 2011, 2011, pp. 1-14, (22.02.2011), https://doi.org/10.48550/arXiv.1102.3052.

Before proceeding further below are the basic formulas to check the sums of **magic** and **bimagic** squares

**Magic Sum**

**Bimagic Sum**

where ** n** is the order the magic square.

### Bimagic Square of Order 8

In this case, we have

**S _{8×8}:=260; Sb_{8×8}:= 11180**

2×4 blocks are of equal sums as of magic square, i.e., 260. See below the **bimagic square** of order 8.

*The construction of *bimagic* square of order 8 is well known in the history, and is done by G. Pfeffermann in 1891. In this case, we have a pandiagonal bimagic square of order 8, where the blocks of order 2×4 are of same sum as of magic square of order 8.*

### Bimagic Square of Order 16

In this case, we have

**S _{16×16}:=2056; Sb_{16×16}:= 351576, S_{4×4}:=(1/4) S_{16×16}=514.**

See below the **bimagic square** of order 16.

### Semi-Bimagic Square of Order 24: Blocks of Order 8

In this case, we have

**S _{24×24}:=6924; Sb_{24×24}:= 2661124 (semi), S_{8×8}:=2308.**

Magic squares of order 8 are of equal sums. These are either bimagic or semi-bimagic. See semi-bimagic square of order 24

### Bimagic Square of Order 32: Blocks of Order 8

In this case, we have

**S _{32×32}:=16400; Sb_{32×32}:= 11201200, S_{8×8}:=4100.**

Magic squares of order 8 are of equal sums. These are either bimagic or semi-bimagic. See **bimagic square** of order 32. It is also pandiagonal.

### Bimagic Square of Order 40: Blocks of Order 8

In this case, we have

**S _{40×40}:=32020; Sb_{40×40}:= 34165340, S_{8×8}:=6404.**

Magic squares of order 8 are of equal sums. These are either bimagic or semi-bimagic. See **bimagic square** of order 40. It is also pandiagonal.

### Semi-Bimagic Square of Order 48: Blocks of Order 16

In this case, we have

**S _{48×48}:=55320; Sb_{48×48}:= 84989960 (semi-bimagic); S_{16×16}:=18440.**

Magic squares of order 16 are of equal sums. These are all **bimagic**. See below **semi-bimagic square** of order 48.

### Bimagic Square of Order 56: Blocks of Order 8

In this case, we have

**S _{56×56}:=87836; Sb_{56×56}:= 183665076; S_{8×8}:=12548.**

Magic squares of order 8 are of equal sums. These are either **bimagic **or** semi-bimagic** squares of order 8. See below **bimagic square** of order 56.

### Bimagic Squares of Order 64: Blocks of Orders 8 and 16

Below are two types of bimagic squares of order 64:

#### First Type: Blocks of Order 8

In this case, we have

**S _{64×64}:=131104; Sb_{64×64}:= 358045024; S_{8×8}:=16338.**

See below **bimagic square** of order 64 with blocks of order 8. These blocks of order 8 are either bimagic or **semi-bimagic** with different sums, but the magic sum of all order magic squares is same.

#### Second Type: Blocks of Order 16

In this case, we have

**S _{64×64}:=131104; Sb_{64×64}:= 358045024; S_{16×16}:=32776 and S_{4×4}:==8194.**

Magic squares of order 16 are of equal sums. These are all **bimagic**. See below **bimagic square** of order 64 with blocks of order 16. These blocks of order 16 are bimagic squares with different sums, but the magic sum of all order 16 magic squares is same.

### Bimagic Square of Order 72: Blocks of Order 8

In this case, we have

**S _{72×72}:=186660; Sb_{72×72}:= 645159180; S_{8×8}:=20740.**

Magic squares of order 8 are of equal sums. These are either bimagic ou semi-bimagic squares of different sums. See the excel sheet given at the end.

### Bimagic Squares of Order 80: Blocks of Orders 8 and 16

Similar to order 64, here also we have two ways to write bimagic square of order 80.

#### First Type: Blocks of Order 8

In this case, we have

**S _{80×80}:=256040; Sb_{80×80}:= 1092522680; S_{8×8}:=25604.**

These blocks of order 8 are either bimagic or **semi-bimagic** with different sums, but the magic sum of all order magic squares is same. See the magic square of order 80 in excel sheet given at the end.

#### Second Type: Blocks of Order 16

In this case, we have

**S _{80×80}:=256040; Sb_{80×80}:= 1092522680; S_{16×16}:=51208 and S_{4×4}:=12802.**

Magic squares of order 16 are of equal sums. See below **bimagic square** of order 80 with blocks of order 16. These blocks of order 16 are **bimagic squares** with different bimagic sums, but the magic sum of all order 16 magic squares is same. See the magic square of order 80 in excel sheet given at the end.

### Bimagic Square of Order 88: Blocks of Order 8

In this case, we have

**S _{88×88}:=340780; Sb_{88×88}:= 1759447140; S_{8×8}:=30980.**

Magic squares of order 8 are of equal sums. These are either **bimagic** ou **semi-bimagic** squares of different sums. See the excel sheet given at the end.

### Bimagic Square of Order 96: Blocks of Order 8

In this case, we have

**S _{96×96}:=442416; Sb_{96×96}:= 2718351376; S_{8×8}:=36868.**

Magic squares of order 8 are of equal sums. These are either **bimagic** ou **semi-bimagic** squares of different sums. See the excel sheet given at the end. ** Even though 96 is divisible by 16, still, we don’t have bimagic square of order 96 with blocks of order 16**.

### Bimagic Square of Order 104: Blocks of Order 8

In this case, we have

**S _{104×104}:=562484; Sb_{104×104}:=4056072124; S_{8×8}:=43268.**

Magic squares of order 8 are of equal sums. These are either **bimagic** ou **semi-bimagic** squares of different sums. See the excel sheet given at the end.

### Bimagic Squares of Order 112: Blocks of Orders 8 and 16

Similar to orders 64 and 80, here also we have two ways to writing **bimagic square** of order 112.

#### First Type: Blocks of Order 8

In this case, we have

**S _{112×112}:=702520; Sb_{112×112}:= 5875174760; S_{8×8}:=50180.**

These blocks of order 8 are either **bimagic** or **semi-bimagic** with different sums, but the magic sum of all order magic squares is same. See the magic square of order 112 in excel sheet given at the end.

#### Second Type: Blocks of Order 16

In this case, we have

**S _{112×112}:=702520; Sb_{112×112}:= 5875174760; S_{16×16}:=100360 and S_{4×4}:=25090.**

See below **bimagic square** of order 80 with blocks of order 16. These blocks of order 16 are **bimagic squares** with different bimagic sums, but the magic sums of all order 16, and order 4 are of equal sums.

### Bimagic Square of Order 120: Blocks of Order 8

In this case, we have

**S _{120×120}:=864060; Sb_{120×120}:=8295264020; S_{8×8}:=57604.**

**bimagic** ou **semi-bimagic** squares of different sums. See the excel sheet given at the end.

### Bimagic Square of Order 128: Blocks of Orders 8 and 16

Similar to orders 64, 80 and 112, here also we have two ways to writing **bimagic square** of order 128.

#### First Type: Blocks of Order 8

In this case, we have

**S _{128×128}:=1048640; Sb_{128×128}:=11454294720; S_{8×8}:=65540.**

These blocks of order 8 are either **bimagic** or **semi-bimagic** with different sums, but the magic sum of all order magic squares is same. See the magic square of order 128 in excel sheet given at the end.

#### Second Type: Blocks of Order 16

In this case, we have

**S _{128×128}:=1048640; Sb_{128×128}:=11454294720;**

**S**and_{16×16}:=131080**32770.****S**_{4×4}:=See below **bimagic square** of order 128 with blocks of order 16. These blocks of order 16 are **bimagic squares** with different bimagic sums, but the magic sums of all order 16, and order 4 are of equal sums.

### Bimagic Square of Order 136: Blocks of Order 8

In this case, we have

**S _{136×136}:=1257796; Sb_{136×136}:=15509882476; S_{8×8}:=73988.**

**bimagic** ou **semi-bimagic** squares of different sums. See the excel sheet given at the end.

### Bimagic Square of Order 144: Blocks of Order 16

In this case, we have

**S _{144×144}:=1493064; Sb_{144×144}:=20640614424;**

**S**and_{16×16}:=165896**41474.****S**_{4×4}:=See below **bimagic square** of order 128 with blocks of order 16. These blocks of order 16 are **bimagic squares** with different bimagic sums, but the magic sums of all order 16, and order 4 are of equal sums.

### Bimagic Square of Order 152: Blocks of Order 8

In this case, we have

**S _{152×152}:=1755980; Sb_{152×152}:=27047359940; S_{8×8}:=92420.**

**bimagic** ou **semi-bimagic** squares of different sums. See the excel sheet given at the end.

### Bimagic Square of Order 160: Blocks of Order 16

In this case, we have

**S _{144×144}:=2048080; Sb_{144×144}:=34954581360;**

**S**and_{16×16}:=**204808****51202.****S**_{4×4}:=See below **bimagic square** of order 128 with blocks of order 16. These blocks of order 16 are **bimagic squares** with different bimagic sums, but the magic sums of all order 16, and order 4 are of equal sums.