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.