Chapter 5 - Polynomials and Factoring - 5.5 Factoring Sums or Differences of Cubes - 5.5 Exercise Set - Page 338: 18

$(2a+1)(4a^2-2a+1)$

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, $ 8a^3+1 ,$ is \begin{array}{l} (2a+1)[(2a)^2-(2a)(1)+(1)^2] \\\\= (2a+1)(4a^2-2a+1) .\end{array}