Answer
$(y-0.5)(y^2+0.5y+0.25)$
Work Step by Step
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, $
y^3-0.125
,$ is
\begin{array}{l}
(y-0.5)[ (y)^2-(y)(-0.5)+(-0.5)^2]
\\\\=
(y-0.5)(y^2+0.5y+0.25)
.\end{array}