Choose any number and write down its divisors:

14

1 2 7 14

Then write down the number of divisors of each of these divisors:

14

1 2 7 14

1 2 2 4

Now the square of the sum of this last group will always equal the sum of its members’ cubes:

(1 + 2 + 2 + 4)2 = 13 + 23 + 23 + 43

Discovered by Joseph Liouville.