\begin{definition}[Definition:Magic Cube]
A '''magic cube''' is an arrangement of the first $n^3$ (strictly) positive integers into an $n \times n \times n$ cubic array such that:
:the sum of the entries in each row in each of the $3$ dimensions
:the sum of the entries along the space diagonals
are the same.
It is not guaranteed that the entries along each of the main diagonals of each plane also sum to the same constant.
 
=== Perfect Magic Cube ===
{{:Definition:Perfect Magic Cube}}
\end{definition}