> The data given include 77053284, which I think I > can prove is the sum of consecutive positive > cubes in only one way (144^3 + ... + 164^3). I think I can prove otherwise. :^) sage: sum(i^3 for i in [1..132]) == 77053284 True sage: sum(i^3 for i in [144..164]) == 77053284 True Doug