Factorize:

$125 a^{3}+\frac{1}{8}=(5 a)^{3}+\left(\frac{1}{2}\right)^{3}$

$=\left(5 a+\frac{1}{2}\right)\left[(5 a)^{2}-5 a \times \frac{1}{2}+\left(\frac{1}{2}\right)^{2}\right]$

$=\left(5 a+\frac{1}{2}\right)\left(25 a^{2}-\frac{5 a}{2}+\frac{1}{4}\right)$