Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.2 - Factoring the Difference of Two Squares - Problem Set 6.2 - Page 249: 84

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

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}