Factorise

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

$=(a x-b)^{3}$

Hence, factorisation of $a^{3} x^{3}-3 a^{2} b x^{2}+3 a b^{2} x-b^{3}$ is $(a x-b)^{3}$.