#### Answer

$(x+1)(x^2-x+1)$

#### Work Step by Step

Using $a^3+b^3=(a+b)(a^2-ab+b^2)$ or the factoring of $2$ cubes, the factored form of the given expression, $
x^3+1
,$ is
\begin{array}{l}\require{cancel}
(x+1)[(x)^2-x(1)+(1)^2]
\\\\=
(x+1)(x^2-x+1)
.\end{array}