You can form (n-1)^{2} 2 by 2 squares.

You can form (n-2)^{2} 3 by 3 squares.

You can form (n-3)^{2} 4 by 4 squares.

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You can form 1^{2} n by n square.

The sum of all these sums is n*(n+1)*(2n+1)/6

Thanks to Guy de Kindler for this one.

Michael Shackleford, A.S.A.