We have,

$a^{3}-8 b^{3}-64 c^{3}-24 a b c$

$=\left\{(a)^{3}+(-2 b)^{3}+(-4 c)^{3}-3(a)(-2 b)(-4 c)\right\}$

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

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

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