Definition:Perfect Magic Cube

Definition
A perfect 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 main diagonal of each plane
 * the sum of the entries along the space diagonals

are the same.

Also known as
A perfect magic cube is often referred to just as a magic cube, but the subject is a large one, and there are several varieties of magic cube which are almost perfect.

Also see

 * Definition:Magic Square