A tetramagic cube is a magic cube that remains magic when all its numbers are squared, cubed, and taken to the fourth power.

Only two tetramagic cubes are known, and both were found by C. Boyer in 2003. The smaller of these is a tetramagic cube of order 1024; this cube, its square, and its cube are perfect, while its fourth power is only semiperfect. The larger is a perfect tetramagic cube of order 8192; this cube, its square, its cube, and its fourth power are perfect.