Three Digit Number

Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?




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Jack thought is enough and he walked to the entry point. The security person said 'eight' , Jack replied smilingly 'four'.
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No Solution

In 2007, a puzzle was released and $2 million prizes were offered for the first complete solution. The competition ended at noon on 31 December 2010, with no solution being found. Wiki