Sum of the cubes of natural numbers.

We can ask ourselves if there Is there a formula to add a sequence of cubes? It seems that the sum is always square, but what is even more remarkable is that the sum of the first n cubes, 13+23+…+ n 3 = ( n ( n +1)/2)2, which is the square of the n th triangle number. For example, 13+23+…+103=(10×11/2)2=552 = 3025.

This interesting lesson will help the ‘AS,’ and the ‘A,’ level pupils to derive a formula to solve the sum of the cubes of natural numbers.