This square has been discovered by Ayliean MacDonald (see links) while attempting to create a magic square of squares.
It's an example of a 3 X 3 square where all rows, columns and diagonals sum to the same number (in this case 29296875), but only the entries in the diagonals are squares.
The Parker Square (A364264) was an attempt (which failed in a different way) to solve the same problem.
