Bimagic Square

If replacing each number by its square in a Magic Square produces another Magic Square, the square is said to be a bimagic square. The first bimagic square (shown above) has order 8 with magic constant 260 for addition and 11,180 after squaring. Bimagic squares are also called Doubly Magic Squares, and are 2-Multimagic Squares.

References

Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, p. 212, 1987.

Hunter, J. A. H. and Madachy, J. S. Mystic Arrays.'' Ch. 3 in Mathematical Diversions. New York: Dover, p. 31, 1975.

Kraitchik, M. Multimagic Squares.'' §7.10 in Mathematical Recreations. New York: W. W. Norton, pp. 176-178, 1942.