Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.2 - Factoring the Difference of Two Squares - Problem Set 6.2 - Page 249: 91

$(1+3a)(1-3a+9a^2)$

Using $a^3+b^3=(a+b)(a^2-ab+b^2)$, or the factoring of the sum of $2$ cubes, the factored form of the given expression, $ 1+27a^3 ,$ is \begin{array}{l}\require{cancel} (1+3a)[(1)^2-1(3a)+(3a)^2] \\\\= (1+3a)(1-3a+9a^2) .\end{array}