perplexus.info :: Numbers : Sum of Cubes

Sum of Cubes (Posted on 2004-05-25)

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

See The Solution Submitted by Gamer

Rating: 3.4000 (5 votes)

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Solution

| Comment 9 of 12 |

1ł+2ł+3ł+....nł=(n(n+1)/2)˛
As n(n+1)/2 is always an integer, the given sum is always a perfect square.

Posted by Praneeth on 2007-08-14 00:55:25

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