64
EDIT: Someone suggested any even number multiplied by itself, but this is not true as the result would not be a cube number. The only number that satisfies the criteria in the question is 64, because;
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It is the smallest composite number that is both a perfect square and a perfect cube.
There is not a number that is a perfect square and perfect cube between 1 and 25.There is not a number that is a perfect square and perfect cube between 1 and 25.There is not a number that is a perfect square and perfect cube between 1 and 25.There is not a number that is a perfect square and perfect cube between 1 and 25.
26, known as Fermat's Sandwich Theorem.
64 = 4 cubed and 8 squared.
It is: 343