Multimagic Cube

An -fold multimagic cube is a magic cube that remains magic when each element is squared, cubed, etc., up to th power. (Of course, when the elements of a cube are taken to a power, the numbers are no longer consecutive, so the resulting magic cube is no longer simple.) A 2-fold multimagic cube is called a bimagic cube, a 3-fold multimagic cube is called a trimagic cube, a 4-fold multimagic cube is called a tetramagic cube, and so on.