This work bring **magic cubes** with six sides as magic squares of orders 3, 4, 5, 7 to 8. Most of the magic squres are with different magic sums. These examples brings only **universal** and or **upside-down** magic cubes. By** universal** we understand that when the magic square is **180 ^{o} rotatable** and are

**mirror looking**, while in case of

**upside-down**the magic squares are only 180

^{o}rotatable.

The readers can also access the following links to download the whole work

**Inder J. Taneja,**Magic Cubes Based on Magic Squares,**Zenodo**, October 17, 2024, pp. 1-63, https://doi.org/10.5281/zenodo.13924915.- Site link: Magic Cubes Based on Magic Squares

**Inder J. Taneja,**Universal and Upside-Down Magic Cubes,**Zenodo**, October 17, 2024, pp. 1-38, https://doi.org/10.5281/zenodo.13947425.- Site Link: Universal and Upside-down Magic Cubes

### Universal and Upside-down Magic Cubes Order 3

### Example 1. Univesal Magic Cube

Let’s consider the following six **semi-magic** squares of order 3

The above six magic squares are constucted using only 3-digits, 2, 5 and 8. All the blocks of order 3×3 are semi-magic with equal semi-magic sum, i.e.,

S_{3×3}(1)=S_{3×3}(2)=S_{3×3}(3)=S_{3×3}(4)=S_{3×3}(5)=S_{3×3}(6):=16665.

Magic cube is composed with six magic squares representing front and back. First three magic squares represent the front part and the last three represent the back part. See below:

Above magic cube is readable in any position, i.e., **upside-down** and/or **mirror looking**.

### Example 2. Univesal Magic Cube

Let’s consider the following six **semi-magic** squares of order 3

The above six magic squares are constucted using only 3-digits, 0, 2 and 5. All the blocks of order 3×3 are **semi-magic** with equal s**emi-magic** sum, i.e.,

S_{3×3}(1)=S_{3×3}(2)=S_{3×3}(3)=S_{3×3}(4)=S_{3×3}(5)=S_{3×3}(6):=7777.

Magic cube is composed with six magic squares representing front and back. First three magic squares represent the front part and the last three represent the back part. See below:

Above magic cube is readable in any position, i.e., **upside-down** and/or **mirror looking**.

### Example 3. Upside-down

Let’s consider the following six **semi-magic** squares of order 3

The above six magic squares are constucted using only 3-digits, 1, 6 and 9. All the blocks of order 3×3 are semi-magic with equal semi-magic sum, i.e.,

S_{3×3}(1)=S_{3×3}(2)=S_{3×3}(3)=S_{3×3}(4)=S_{3×3}(5)=S_{3×3}(6):=17776.

Magic cube is composed with six magic squares representing front and back. First three magic squares represent the front part and the last three represent the back part. See below:

Above magic cube is **upside-down**, i.e, 180 degrees rotation, still we can read each magic square.

### Example 4. Upside-down

Let’s consider the following six **semi-magic** squares of order 3

The above six magic squares are constucted using only 3-digits, 6, 8 and 9. All the blocks of order 3×3 are semi-magic with equal semi-magic sum, i.e.,

S_{3×3}(1)=S_{3×3}(2)=S_{3×3}(3)=S_{3×3}(4)=S_{3×3}(5)=S_{3×3}(6):=25553.

Above magic cube is **upside-down**, i.e, 180 degrees rotation, still we can read each magic square.

### Magic Cubes with Magic Squares of Order 4

### Example 1. Upside-down Magic Cube

Let’s consider the following six **magic **squares of order 4:

The above six magic squares are constucted using only 4-digits, 1, 6, 8 and 9. All the blocks of order 4×4 are magic squares with equal magic sum, i.e.,

S_{4×4}(1)=S_{4×4}(2)=S_{4×4}(3)=S_{4×4}(4)=S_{4×4}(5)=S_{4×4}(6):=26664.

Above magic cube is readable **upside-down** position.

### Example 2. Universal Magic Cube

Let’s consider the following six **magic **squares of order 4:

The above six magic squares are constucted using only 4-digits, 1, 2, 5 and 8. All the blocks of order 4×4 are magic squares with equal magic sum, i.e.,

S_{4×4}(1)=S_{4×4}(2)=S_{4×4}(3)=S_{4×4}(4)=S_{4×4}(5)=S_{4×4}(6):=17776.

Above magic cube is universal, i.e., it is readable as **upside-down** and/or **mirror looking** position.

### Example 3. Universal Magic Cube

Let’s consider the following six **magic **squares of order 4:

The above six magic squares are constucted using only 4-digits, 0, 2, 5 and 8. All the blocks of order 4×4 are magic squares with equal magic sum, i.e.,

S_{4×4}(1)=S_{4×4}(2)=S_{4×4}(3)=S_{4×4}(4)=S_{4×4}(5)=S_{4×4}(6):=16665.

Above magic cube is universal, i.e., it is readable as **upside-down** and/or **mirror looking** position.

### Magic Cubes with Magic Squares of Order 5

### Example 1. Upside-side Magic Cube

Let’s consider the following six **pandiagonal **magic squares of order 5

The above six magic squares are constucted using only 4-digits, 1, 6, 8 and 9. All the blocks of order 5×5 are **pandiagonal** magic squares with different magic sum, i.e.,

S_{5×5}(1):=34352, S_{5×5}(2):=35653, S_{5×5}(3):=35540, S_{5×5}(4):=35640, S_{5×5}(5):=35552 and S_{5×5}(6):=34353.

Above magic cube is readable **upside-down** position.

### Example 2. Universal Magic Cube

Let’s consider the following six **pandiagonal **magic squares of order 5

The above six magic squares are constucted using only 4-digits, 0, 2, 5 and 8. All the blocks of order 5×5 are pandiagonal magic squares with different magic sum, i.e.,

S_{5×5}(1):=15953, S_{5×5}(2):=25250, S_{5×5}(3):=25457, S_{5×5}(4):=25157, S_{5×5}(5):=25553 and S_{5×5}(6):=25553.

Above magic cube is **universal,** i.e., it is readable as **upside-down** and/or **mirror looking** position.

### Example 3. Universal Magic Cube

Let’s consider the following six **pandiagonal **magic squares of order 5

The above six magic squares are constucted using only 4-digits, 1, 2, 5 and 8. All the blocks of order 5×5 are pandiagonal magic squares with different magic sum, i.e.,

S_{5×5}(1):=17064, S_{5×5}(2):=26361, S_{5×5}(3):=26568, S_{5×5}(4):=26268, S_{5×5}(5):=26664 and S_{5×5}(6):=17061.

Above magic cube is **universal**, i.e., it is readable as **upside-down** and/or **mirror looking** position.

### Magic Cubes with Magic Squares of Order 7

### Example 1. Universal Magic Cube

Let’s consider the following six **pandiagonal **magic squares of order 7

The above six magic squares are constucted using only 5-digits, 0, 1, 2, 5 and 8. All the blocks of order 7×7 are **pandiagonal** magic squares with different magic sum, i.e.,

S_{7×7}(1):=27472, S_{7×7}(2):=27449, S_{7×7}(3):=27449, S_{7×7}(4):=27471, S_{7×7}(5):=25171 and S_{7×7}(6):=27371.

Above magic cube is **universal**, i.e., it is readable as **upside-down** and/or **mirror looking** position.

### Example 2. Upside-down Magic Cube

Let’s consider the following six **pandiagonal **magic squares of order 7

The above six magic squares are constucted using only 5-digits, 2, 5, 6, 8 and 9. All the blocks of order 7×7 are **pandiagonal** magic squares with different magic sum, i.e.,

S_{7×7}(1):=47470, S_{7×7}(2):=47463, S_{7×7}(3):=47463, S_{7×7}(4):=47475, S_{7×7}(5):=46775 and S_{7×7}(6):=47975.

Above **magic cube is** readable as **upside-down.**

### Example 3. Upside-down Magic Cube

Let’s consider the following six **pandiagonal **magic squares of order 7

The above six magic squares are constucted using only 5-digits, 0, 1, 6, 8 and 9. All the blocks of order 7×7 are **pandiagonal** magic squares with different magic sum, i.e.,

S_{7×7}(1):=36360, S_{7×7}(2):=36417, S_{7×7}(3):=42060, S_{7×7}(4):=36367, S_{7×7}(5):=42067 and S_{7×7}(6):=37067.

Above **magic cube is** readable as **upside-down.**

### Magic Cubes with Magic Squares of Order 8

### Example 1. Upside-down Magic Cube

Let’s consider the following six magic squares of order 8

The above six magic squares are constucted using only 5-digits, 0, 1, 6, 8 and 9. The First four magic squares are of equal magic sums, and the last two are also of equal magic sums. See below;

S_{8×8}(1):=44238, S_{8×8}(2):=44238, S_{8×8}(3):=44238, S_{8×8}(4):=44238, S_{8×8}(5):=44244 and S_{8×8}(6):=44244.

Above **magic cube is** readable as **upside-down.**

### Example 2. Upside-down Magic Cube

Let’s consider the following six magic squares of order 8

The above six magic squares are constucted using only 5-digits, 2, 5, 6, 8 and 9. The First four magic squares are of equal magic sums, and the last two are also of equal magic sums. See below;

S_{8×8}(1):=55146, S_{8×8}(2):=55146, S_{8×8}(3):=55146, S_{8×8}(4):=55146, S_{8×8}(5):=55136 and S_{8×8}(6):=55136.

Above **magic cube is** readable as **upside-down.**

### Example 3. Universal Magic Cube

Let’s consider the following six magic squares of order 8

The above six magic squares are constucted using only 5-digits, 0, 1, 6, 8 and 9. The First four magic squares are of equal magic sums, and the last two are also of equal magic sums. See below;

S_{8×8}(1):=32046, S_{8×8}(2):=24846, S_{8×8}(3):=24918, S_{8×8}(4):=32118, S_{8×8}(5):=32118 and S_{8×8}(6):=32094.

Above magic cube is **universal**, i.e., it is readable as **upside-down** and/or **mirror looking** position.