Magic Constant of Magic Cube

Theorem
The magic constant of a magic cube of order $n$ is given by:


 * $C_n = \dfrac {n \paren {n^3 + 1} } 2$

Proof
Let $M_n$ denote a magic cube of order $n$.

By Sum of Terms of Magic Cube, the total of all the entries in $M_n$ is given by:


 * $T_n = \dfrac {n^3 \paren {n^3 + 1}} 2$

There are $n^2$ rows in $M_n$, each one with the same magic constant.

Thus the magic constant $C_n$ of the magic cube $M_n$ is given by: