Answer
$(9+x)(81-9x+x^2)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
729+x^3
,$ use the factoring of the sum/difference of $2$ cubes.
$\bf{\text{Solution Details:}}$
Using $(a\pm b)(a^2\mp ab+b^2)$ or the factoring of the sum/difference of $2$ cubes, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(9+x)[(9)^2-9(x)+(x)^2]
\\\\=
(9+x)(81-9x+x^2)
.\end{array}