FERMAT QUESTION

Fermat conerned about number 26, for its position. Indeed 26 is between a cube 27 and a square 25.He wondered if there exist another numbers with this feature. In the margin of a page of Diphanto's arithmetic, as he usualy didl, wrote that had found a demonstration makes sure no others number exists,that there is only 26 with this feature. Who can prove it?

Thank you.

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