Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$-8a^{6}$
Using the laws of exponents, the given expression, $\left( -2a^2 \right)^{3} ,$ simplifies to \begin{array}{l}\require{cancel} (-2)^3a^{2(3)} \\\\= -8a^{6} .\end{array}