Factor
\frac{\left(2a+1\right)\left(4a^{2}-2a+1\right)}{8}
Evaluate
a^{3}+\frac{1}{8}
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\frac{8a^{3}+1}{8}
Factor out \frac{1}{8}.
\left(2a+1\right)\left(4a^{2}-2a+1\right)
Consider 8a^{3}+1. Rewrite 8a^{3}+1 as \left(2a\right)^{3}+1^{3}. The sum of cubes can be factored using the rule: p^{3}+q^{3}=\left(p+q\right)\left(p^{2}-pq+q^{2}\right).
\frac{\left(2a+1\right)\left(4a^{2}-2a+1\right)}{8}
Rewrite the complete factored expression. Polynomial 4a^{2}-2a+1 is not factored since it does not have any rational roots.
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