[aways]

One night while bored, I "discovered" the following relation (turns out it's well known; not original to me):

The sum of the cubes of the first N integers is equal to the square of the sum of the first N integers.

For example, take N=3:

{Sum_i=1 to 3} i^3 = [{Sum_i=1 to 3}]^2

1 + 8 + 27 = [1+2+3]^2

36 = 36

Can anybody prove the general relation?