Answer
$y(3x+2)(9x^{2}-6x+4)$
Work Step by Step
$ 27x^{3}y+8y\qquad$...factor out $y$.
$=y(27x^{3}+8)\qquad$...use the sum of two cubes:
$\mathrm{A}^{3}+\mathrm{B}^{3} = (\mathrm{A}+\mathrm{B})(\mathrm{A}^{2} - \mathrm{A}\mathrm{B} + B^{2})$
$=y((3x)^{3}+2^{3})$
$=y(3x+2)(9x^{2}-6x+4)$
