Compute the prime factorization of $25^{3}-27^{2}$.
Noticing that $25=5^{2}$ and $27=3^{3}$, we have this is

$$
\begin{aligned}
5^{6}-3^{6} & =\left(5^{3}-3^{3}\right)\left(5^{3}+3^{3}\right) \\
& =(5-3)\left(5^{2}+5 \cdot 3+3^{2}\right)(5+3)\left(5^{2}-5 \cdot 3+3^{2}\right) \\
& =2 \cdot 49 \cdot 8 \cdot 19 \\
& =2^{4} \cdot 7^{2} \cdot 19 .
\end{aligned}
$$