# Cube related to squares!

Problem:

Show that the cube of a positive integer can always be written as the difference of two squares!

Proof:

We only need to observe that

$n^{3} = (1^{3}+2^{3}+3^{3}+ \ldots + n^{3}) - (1^{3}+2^{3}+3^{3}+ \ldots + (n-1)^{3})$

which, in turn, equals $(\frac{n(n+1)}{2})^{2}-(\frac{(n-1)(n)}{2})^{2}$.

Hooray ! 🙂 That’s all !

Nalin Pithwa

## One thought on “Cube related to squares!”

1. Masst chhe, Baapu!

Like

This site uses Akismet to reduce spam. Learn how your comment data is processed.