Factorise:

$3 \sqrt{3} a^{3}-b^{3}-5 \sqrt{5} c^{3}-3 \sqrt{15} a b c$

$=(\sqrt{3} a)^{3}+(-b)^{3}+(-\sqrt{5} c)^{3}-3(\sqrt{3} a)(-b)(-\sqrt{5} c)$

We know

$x^{3}+y^{3}+z^{3}-3 x y z=(x+y+z)\left(x^{2}+y^{2}+z^{2}-x y-y z-z x\right)$

Here, $x=(\sqrt{3} a), y=(-b), z=(-\sqrt{5} c)$

$3 \sqrt{3} a^{3}-b^{3}-5 \sqrt{5} c^{3}-3 \sqrt{15} a b c$

$=(\sqrt{3} a)^{3}+(-b)^{3}+(-\sqrt{5} c)^{3}-3(\sqrt{3} a)(-b)(-\sqrt{5} c)$

$=(\sqrt{3} a-b-\sqrt{5} c)\left(3 a^{2}+b^{2}+5 c^{2}+\sqrt{3} a b-\sqrt{5} b c+\sqrt{15} c\right)$