The existence or not of a non-trivial integer 3x3 magic square of squares is STILL an unsolved problem. As far as I know, the issue was researched for a set of all integers below 10^14.

Let's go for a lesser challenge: the 3 columns, 3 rows and only one of the diagonals has to sum up to the same value.
It is still a D4 problem, if I do not release any hints.

Go for it!