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

Below are **bimagic squares** written in blocks multiples of orders 16. This work brings bimagic squares multiples of 16, such as, of orders 400, 800, 1600 and 2000. Most of the work is done manually by author in 2011. 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.

Before presenting **bimagic squares** of orders 400, 800, 1600 and 2000, below is an example of bimagic square of order 16.

### Bimagic Square of Order 16

In this case, we have

**S _{16×16} := 2056 and Sb_{16×16} := 351576, **

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

Magic squares of order 4 are of equal sums, **S _{4×4} :=(1/4) S_{16×16}=514.**

### Bimagic Square of Order 400: Blocks of Order 16

**Bimagic square of order 400×400** has the the following properties:

- 4×4 are
**magic squares**with**equal magic sums**, i.e.,**S**_{4×4}:=320002 - 16×16 are
**bimagic squares**with**equal magic**and**different bimagic sums**, i.e.,**S**._{16×16}:=1280008 - 80×80 are
**bimagic squares**with**equal magic**and**different bimagic sums**, i.e.,**S**._{80×80}:=6400040 - 400×400 is a
**bimagic square**with**magic and bimagic sums**, i.e.,**S**and_{256×256}:=32000200**Sb**._{256×256}:=3413365333400

Summarizing, we have a **bimagic square of order 400×400**, where blocks of orders 4×4, 16×16 and 80×80 are of equal magic sums. The magic squares of orders 16×16 and 80×80 are bimagic with different bimagic sums. These values are given in tables in an excel sheet attached with the work.

**Excel file for download**

### Bimagic Square of Order 800: Blocks of Order 16

**Bimagic square of order 800×800** has the the following properties:

- 4×4 are
**magic squares**with**equal magic sums**, i.e.,**S**_{4×4}:=1280002 - 16×16 are
**bimagic squares**with**equal magic**and**different bimagic sums**, i.e.,**S**._{16×16}:=5120008 - 160×160 are
**bimagic squares**with**equal magic**and**different bimagic sums**, i.e.,**S**._{160×160}:=51200080 - 800×800 is a
**bimagic square**with**magic and bimagic sums**, i.e.,**S**and_{800×800}:=256000400**Sb**._{800×800}:=109226922666800

Summarizing, we have a **bimagic square of order 800×800**, where blocks of orders 4×4, 16×16 and 160×160 are of equal magic sums. The magic squares of orders 16×16 and 160×160 are bimagic with different bimagic sums. These values are given in tables in an excel sheet attached with the work.

**Excel file for download**

### Bimagic Square of Order 1600: Blocks of Order 16

**Bimagic square of order 1600×1600** has the the following properties:

- 4×4 are
**magic squares**with**equal magic sums**, i.e.,**S**_{4×4}:=5120002 - 16×16 are
**bimagic squares**with**equal magic**and**different bimagic sums**, i.e.,**S**._{16×16}:=20480008 - 80×80 are
**bimagic squares**with**equal magic**and**different bimagic sums**, i.e.,**S**._{80×80}:=102400040 - 400×400 are
**bimagic squares**with**equal magic**and**different bimagic sums**, i.e.,**S**512000200._{400×400}:= - 1600×1600 is a
**bimagic square**with**magic and bimagic sums**, i.e.,**S**and_{1600×1600}:=2048000800**Sb**._{1600×1600}:=3495255381333600

Summarizing, we have a **bimagic square of order 1600×1600**, where blocks of orders 4×4, 16×16, 80×80 and 400×400 are of equal magic sums. The magic squares of orders 16×16, 80×80 and 400×400 are bimagic with different bimagic sums. These values are given in tables in an excel sheet attached with the work.

**Excel file for download**

### Bimagic Square of Order 2000: Blocks of Order 16

**Bimagic square of order 2000×2000** has the the following properties:

- 4×4 are
**magic squares**with**equal magic sums**, i.e.,**S**_{4×4}:=8000002 - 16×16 are
**bimagic squares**with**equal magic**and**different bimagic sums**, i.e.,**S**._{16×16}:=32000008 - 80×80 are
**bimagic squares**with**equal magic**and**different bimagic sums**, i.e.,**S**._{80×80}:=160000040 - 400×400 are
**bimagic squares**with**equal magic**and**different bimagic sums**, i.e.,**S**._{400×400}:=800000200 - 1600×1600 is a
**bimagic square**with**magic and bimagic sums**, i.e.,**S**and_{2000×2000}:=4000001000**Sb**_{2000×2000}:=**.**

Summarizing, we have a **bimagic square of order 2000×2000**, where blocks of orders 4×4, 16×16, 80×80 and 400×400 are of equal magic sums. The magic squares of orders 16×16, 80×80 and 400×400 are bimagic with different bimagic sums. These values are given in tables in an excel sheet attached with the work.

**Excel file for download**

### References:

**Inder J. Taneja,**Block-Wise Construction of Bimagic Squares: Multiples of Orders 8 and 16.**Inder J. Taneja,**Block-Wise Construction of Bimagic Squares Multiples of 25: Orders 25, 125 and 625.**Inder J. Taneja,**Block-Wise Construction of Bimagic Squares Multiples of 9: Orders 9, 81 and 729.**Inder J. Taneja,**Block-Wise Construction of Bimagic Squares of Orders 121 and 1331.**Inder J. Taneja,**Bimagic Squares of Orders 256, 512 and 1024: Blocks of Order 16.**Inder J. Taneja,**Bimagic Squares of Orders 200 and 1000: Blocks of Order 8**Inder J. Taneja,**Bimagic Squares of Orders 400, 800, 1600 and 2000: Blocks of Order 16. (This work)