It can be shown that if a magic cube consists of the numbers 1, 2, ..., n3, then it has magic constant (sequence A027441 in the OEIS) M 3 ( n ) = n ( n 3 + 1 ) 2 . {\displaystyle M_{3}(n)={\frac {n(n^{3}+1)}{2}}.} If, in addition, the numbers on every cross section diagonal also sum up to the cube's magic number, the cube is called a perfect magic cube; otherwise, it is called a semiperfect magic cube.
若魔術立方體由數列1, 2, ..., n3構成，則可以證明其幻方常數為（OEIS中的数列A027441） M 3 ( n ) = n ( n 3 + 1 ) 2 {\displaystyle M_{3}(n)={\frac {n(n^{3}+1)}{2}}} 另外，如果每個截面對角線上的數字之和亦等於幻方常數，則稱此立方體為完美魔方（英语：perfect magic cube）；否則，稱其為半完美魔方（英语：semiperfect magic cube）。