How do you factor w^3-27?

${w}^{3} - 27 = \left(w - 3\right) \left({w}^{2} + 3 w + 9\right)$

Explanation:

Use the formula for "difference of 2 cubes"

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

Let $a = w$ and $b = 3$
because ${a}^{3} = {w}^{3}$ and ${b}^{3} = {3}^{3} = 27$

then

${w}^{3} - 27 = \left(w - 3\right) \left({w}^{2} + 3 w + 9\right)$

God bless....I hope the explanation is useful..