Bimagic squares

A bimagic square is first of all a normal magic square, in which the rows, columns and diagonals give a constant sum. In this example the sum is always S8=260.

bimagic square: sums

But if all integers are raised to the second power, all rows, columns and diagonals have still a constant sum result. In this example we have S82=11180.

bimagic square: qudratic sum

Generally the biquadratic sum is given by the following formula:

bimagic square: sums