Can you partition the numbers 1, 2, 3, ... nē in n separate subsets, each with n numbers, all subsets having the same sum?

(In reply to

The Odd-Sided Squares Principle by Bruno)

There is a classical algorithm for filling such a magic square -- and
you may have rediscovered it, or invented a new one altogether. The
method I know of, implies imposing another square on the original, but
at 45 degrees, then filling this with the numbers from 1 to n^2 in a
certain way, and finally moving the numbers from the big square to the
original one.