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.)