$a, b$ are two naturals such that,
$a^{2}-b^{2}=k^{3}$ and $a^{3}-b^{3}=c^{2}$
where $k^{3}$ and $c^{2}$ are perfect cube and square respectively.
What can be the least possible pair of naturals $(a, b)$ for the above to hold true?
This link suggests $(10, 6)$ but I'm not satisfied with the answer. Please help.