How do you factor 2y^3 - 54z^3?

$2 {y}^{3} - 54 {z}^{3} = 2 \left({y}^{3} - 27 {z}^{3}\right) = 2 \left(y - 3 z\right) \left({y}^{2} + 3 y z + 9 {z}^{2}\right)$
${a}^{3} - {b}^{3} = \left(a - b\right) \left({a}^{2} + a b + {b}^{2}\right)$ (check this by expanding the right hand side).
For the expression ${y}^{3} - 27 {z}^{3}$, use $a = y$ and $b = 3 z$.