cubes and cube roots

Well...I could multiply by (1/25) and that would give us

33275 *(1/25) = 1331 and that's a perfect cube of 11

Or...I could multiply by 0   and that would give us

33275 * 0 = 0    and that's the perfect cube of 0

Or...I could multiply by -5 and that would give us

-166375 and that's a perfect cube of (-55)

Is this what you were asking??.....Is there a "smallest" number??

First look at the prime factors of 33275

$${factorize}{\left({\mathtt{33\,275}}\right)} \Rightarrow \left\{ \begin{array}{l}{\mathtt{25}} = {{\mathtt{5}}}^{{\mathtt{2}}}\\ {\mathtt{1\,331}} = {{\mathtt{11}}}^{{\mathtt{3}}}\\ \end{array} \right\}$$

i.e.  $$33275=5^2*11^3$$

This should give you a clue.

I suspect the questioner had positive integers in mind!