Prove that the sum of consecutive perfect cubes (starting with 1) is always a perfect square.

For example:
1=1
1+8=9
1+8+27=36

the sum of cubes of the set of consecutive numbers is equal to square of their sum...this is the well known equality which can be proved using the theory of induction.

1 cubed =1= 1 squred

1 cubed+2 cubed = 1+8 = 9 = 3 square = (1+2) whole squared.

1 cubed + 2 cubed + 3 cubed = 1+8+27 = 36 = 6 squared = (1+2+3) whole squared.

So sum of consecutive perfect cubes (starting with 1) is always a perfect square.

Posted by Pemmadu Raghu Ramaiah on 2005-01-09 02:45:14