A bimagic cube is a (normal) magic cube that remains magic when all its elements are squared. Of course, even a normal magic cubic becomes nonnormal (i.e., contains nonconsecutive elements) upon squaring.
Cazalas (1934) attempted but failed to construct a bimagic cube (Boyer). David M. Collison apparently constructed a bimagic cube of order 25 in an unpublished paper (Hendricks 1992), but it was not until the year 2000 that John Hendricks published an order 25 perfect magic cube whose square is a semiperfect magic cube.
On January 20, 2003, Christian Boyer discovered an order 16 bimagic cube (where the cube itself is perfect magic, but its square is only semiperfect magic). This was rapidly followed by another order 16 bimagic cube (where the base cube is perfect and its square semiperfect) on January 23, an order 32 bimagic cube (where both the base cube and its square are perfect) on January 27, and an order 27 bimagic cube (where the base cube is perfect but its square is semiperfect) on February 3, 2003.
Boyer's 16-cubes thus became the smallest known bimagic cube, and his order 32 cube became the first known perfect bimagic cube.
. Paris: Hermann, 1934.Danielsson, H. "Printout
of a Bimagic Cube: Order 25."