Factorise:

$2 \sqrt{2} a^{3}+3 \sqrt{3} b^{3}+c^{3}-3 \sqrt{6} a b c$

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

We know

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

$x=\sqrt{2} a, y=\sqrt{3} b, z=c$

$(\sqrt{2} a)^{3}+(\sqrt{3} b)^{3}+c^{3}-3(\sqrt{2} a)(\sqrt{3} b) c$

$=(\sqrt{2} a+\sqrt{3} b+c)\left(2 a^{2}+3 b^{2}+c^{2}-\sqrt{6 a b}-\sqrt{3 b c}-\sqrt{2} a c\right)$