The value of $27 a^3-2 \sqrt{2} b^3$ is equal to:

$(3 a-\sqrt{2} b)\left(9 a^2-2 b^2+6 \sqrt{2} a b\right)$ $(3 a-\sqrt{2} b)\left(9 a^2+2 b^2+6 \sqrt{2} a b\right)$ $(3 a-\sqrt{2} b)\left(9 a^2+2 b^2+3 \sqrt{2} a b\right)$ $(3 a-\sqrt{2} b)\left(9 a^2-2 b^2-3 \sqrt{2} a b\right)$

$(3 a-\sqrt{2} b)\left(9 a^2+2 b^2+3 \sqrt{2} a b\right)$

We know that, a3 – b3 = (a – b) (a2 + b2 + ab) = 27a3 - 2√2 b3 = $(3 a-\sqrt{2} b)\left(9 a^2+2 b^2+3 \sqrt{2} a b\right)$