Factorise

$a^{3}-12 a(a-4)-64=a^{3}-12 a^{2}+48 a-64$

$=(a)^{3}-(4)^{3}-3(a)^{2}(4)+3(a)(4)^{2}$

$=(a-4)^{3}$

Hence, factorisation of $a^{3}-12 a(a-4)-64$ is $(a-4)^{3}$.