#### Answer

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

#### Work Step by Step

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}