Factorize:

$216+27 b^{3}+8 c^{3}-108 a b c=(6)^{3}+(3 b)^{3}+(2 c)^{3}-3 \times 6 \times 3 b \times 2 c$

$=(6+3 b+2 c)\left[6^{2}+(3 b)^{2}+(2 c)^{2}-6 \times 3 b-3 b \times 2 c-2 c \times 6\right]$

$=(6+3 b+2 c)\left(36+9 b^{2}+4 c^{2}-18 b-6 b c-12 c\right)$