Arrange the first n² odd numbers in a square (here n = 6):

 1  3  5  7  9 11
13 15 17 19 21 23
25 27 29 31 33 35
37 39 41 43 45 47
49 51 53 55 57 59
61 63 65 67 69 71

Now, no matter n, the sum of the first row is n², the sum of either long diagonal is n³, and the sum of the whole array is n⁴.

(From Edward Barbeau’s Power Play, 1997.)