#### Answer

$(2p +3 )(4p^2-6p +9 )$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To factor the given expression, $
8p^3+27
,$ use the factoring of the sum of $2$ cubes.
$\bf{\text{Solution Details:}}$
The expressions $
8p^3
$ and $
27
$ are both perfect cubes (the cube root is exact). Hence, $
8p^3+27
,$ is a sum of $2$ cubes. Using the factoring of the sum of $2$ cubes which is given by $a^3+b^3=(a+b)(a^2-ab+b^2),$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
(2p )^3+(3 )^3
\\\\=
(2p +3 )[(2p )^2-2p (3 )+(3 )^2]
\\\\=
(2p +3 )(4p^2-6p +9 )
.\end{array}