解：
(1)
$\begin{aligned}a^{3}-3a^{2}+6a - 18&=a^{2}(a - 3)+6(a - 3)\\&=(a - 3)(a^{2}+6)\end{aligned}$
(2)
因为$m + n = 5，$$m - n = 1，$
$\begin{aligned}m^{2}-n^{2}+2m - 2n&=(m + n)(m - n)+2(m - n)\\&=(m - n)(m + n + 2)\\&=1\times(5 + 2)\\&=7\end{aligned}$
