175. Squares and cubes. Can you find two numbers, the difference of whose squares is a cube, and the difference of whose cubes is a square? What are the two smallest numbers with this property?
175. The smallest possible solution has the form

\[
\begin{aligned}
& 10^{2}-6^{2}=100-36=64=4^{3} \\
& 10^{3}-6^{3}=1000-216=784=28^{2}
\end{aligned}
\]