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Let the square of an integer be represented as (a³)² and
the cube of the other integer be represented as (a²)³.

So we simply look for a three-digit number that is the sixth power of another integer.

1⁶, 2⁶, 3⁶, 4⁶ , ...
1, 64, 729, 4096, ...

So the 3 digit number is 729 which is the cube of 9 and the square of 27
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