Resizing a matrix

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I have a problem of resizing a rectangular matrix into a square matrix with certain restrictions: Suppose you have a rectangle of size $m\times n$, and wlog $m> n$. Now i want to resize this rectangle into square i.e the the new length should be $m'\times m'$. The new length can be obtained by adding zero rows and zero columns. The extra condition is that $m'{^2}$ should be a perfect cube. How can this be solved can somebody hint?.

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$m'^2$ is a cube means $m'$ is a cube as well, so just find the next cubic number $\ge m$.