I was challenged last week by a math professor at a local college to prove one of "his" discoveries. He said he could not prove it, and I must admit that I am lousy at math proofs. The following statement appears true because I wrote a VB6 program for the first 100 whole numbers and it checks out:

"The sums of the cubes of the first N whole numbers equals the sums of these same N numbers squared."

e.g.,
1^3 + 2^3 = (1 + 2)^2 = 9
1^3 + 2^3 + 3^3 = (1 + 2 + 3)^2 = 36
1^3 + 2^3 + 3^3 + 4^3 = (1 + 2 + 3 + 4)^2 = 100
1^3 + 2^3 + 3^3 + 4^3 + 5^3 = (1 + 2 + 3 + 4 + 5)^2 = 225

and so on until the cows come home or even double precision overflows. Can this be proven?