\[x^{3} + 27y^{3} - 3x^{2}y - 9xy^{2} =\]
\[= (x + 3y)\left( x^{2} - 3xy + 9y^{2} \right) - 3xy(x + 3y) =\]
\[= (x + 3y)\left( x^{2} - 3xy + 9y^{2} - 3xy \right) =\]
\[(x + 3y)\left( x^{2} - 6xy + 9y^{2} \right) =\]
\[= (x + 3y)(x - 3y)^{2}\]