$\begin{array}{l}\phantom{\phantom{;}3m^{2}+2;}{\phantom{;}27m^{6}\phantom{-;x^n}-18m^{4}\phantom{-;x^n}+12m^{2}\phantom{-;x^n}-8\phantom{;}\phantom{;}}\\\phantom{;}3m^{2}+2\overline{\smash{)}\phantom{;}81m^{8}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-16\phantom{;}\phantom{;}}\\\phantom{\phantom{;}3m^{2}+2;}\underline{-81m^{8}\phantom{-;x^n}-54m^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-81m^{8}-54m^{6};}-54m^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-16\phantom{;}\phantom{;}\\\phantom{\phantom{;}3m^{2}+2-;x^n;}\underline{\phantom{;}54m^{6}\phantom{-;x^n}+36m^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}54m^{6}+36m^{4}-;x^n;}\phantom{;}36m^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-16\phantom{;}\phantom{;}\\\phantom{\phantom{;}3m^{2}+2-;x^n-;x^n;}\underline{-36m^{4}\phantom{-;x^n}-24m^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-36m^{4}-24m^{2}-;x^n-;x^n;}-24m^{2}\phantom{-;x^n}-16\phantom{;}\phantom{;}\\\phantom{\phantom{;}3m^{2}+2-;x^n-;x^n-;x^n;}\underline{\phantom{;}24m^{2}\phantom{-;x^n}+16\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}24m^{2}+16\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\\\end{array}$

$27m^{6}-18m^{4}+12m^{2}-8$