Sum of Terms of Magic Cube

Theorem
The total of all the entries in a magic cube of order $n$ is given by:


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

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

$M_n$ is by definition an arrangement of the first $n^3$ (strictly) positive integers into an $n \times n \times n$ cubic array containing the positive integers from $1$ upwards.

Thus there are $n^3$ entries in $M_n$, going from $1$ to $n^3$.

Thus: