Factorize:

$a^{3}+8 b^{3}+64 c^{3}-24 a b c=a^{3}+(2 b)^{3}+(4 c)^{3}-3 \times a \times 2 b \times 4 c$

$=(a+2 b+4 c)\left[a^{2}+(2 b)^{2}+(4 c)^{2}-a \times 2 b-2 b \times 4 c-4 c \times a\right]$

$=(a+2 b+4 c)\left(a^{2}+4 b^{2}+16 c^{2}-2 a b-8 b c-4 c a\right)$