Answer
$5x(25x^2+15x+3)$
Work Step by Step
Since the polynomial $(5x + 1)^3 - 1$ is a difference of two cubes, we have
$$
(5x + 1)^3 - 1=(5x+1 -1)((5x+1)^2+(5x+1)+1)\\
=(5x)(25x^2+10x+1+5x+1+1)\
=5x(25x^2+15x+3)
.$$
where we used the formula $(x-y)^3=(x-y)(x^2+xy+y^2)$.
The polynomial $25x^2+15x+3$ can not be factored further since it is prime.
