Multimagic cube
In mathematics, a P-multimagic cube is a magic cube that remains magic even if all its numbers are replaced by their kth powers for 1 ≤ k ≤ P. 2-multimagic cubes are called bimagic, 3-multimagic cubes are called trimagic, and 4-multimagic cubes tetramagic. A P-multimagic cube is said to be semi-perfect if the kth power cubes are perfect for 1 ≤ k < P, and the Pth power cube is semiperfect.