A magic cube is an n×n×n version of a magic square in which the n^2 rows, n^2 columns, n^2 pillars, and four space diagonals each sum to a single number M_3(n) known as the cube's magic constant. Magic cubes are most commonly assumed to be "normal, " i.e., to have elements that are the consecutive integers 1, 2, ..., n^3. However, this requirement is dropped (as it must be) in the consideration of so-called multimagic cubes. If it exists, a normal magic cube has magic constant M(n) = 1/2 n(n^3 + 1).
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