(1) A + C = B + D

(2) A + B’= B + A’

(3) B + C’= C + B’

(4) C + D’= D + C’

(5) D + A’= A + D’

(6) A’+ C’= B’+ D’

With a bit of algebra, we can easily derive a seventh equation

(7) A + C’= B + D’= C + A’= D + B’

which states that in a Balanced Cube the sums along the diagonals of the cube are equal.

Let’s take equation (1) and 1 + 4 = 2 + 3 (which leaves 5 + 8 = 6 + 7)

A = 1 –> C = 4

B = 2 –> D = 3

Now we substitute A, B, C, and D in equation (7)

1 + C’= 2 + D’= 4 + A’= 3 + B’ –> A’= 5, B’= 6, C’=8, and D’=7

So 1-2-4-3/5-6-8-7 and the sum along the diagonals of the cube is 9

PS: checking the balancing equations

(1) 1 + 4 = 2 + 3

(2) 1 + 6 = 2 + 5

(3) 2 + 8 = 4 + 6

(4) 4 + 7 = 3 + 8

(5) 3 + 5 = 1 + 7

(6) 5 + 8 = 6 + 7