Answer
$(2x+3y)(4x^2-6xy+9y^2)$
Work Step by Step
Using $a^3+b^3=(a+b)(a^2-ab+b^2)$ or the factoring of the sum of two cubes, the given expression, $
8x^3+27y^3
$ is equivalent to
\begin{array}{l}\require{cancel}
&
(2x)^3+(3y)^3
\\&=
(2x+3y)\left((2x)^2-(2x)(3y)+(3y)^2\right)
\\&=
(2x+3y)(4x^2-6xy+9y^2)
.\end{array}
Hence, the factored form of $
8x^3+27y^3
$ is $
(2x+3y)(4x^2-6xy+9y^2)
$.
