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2\left(ay^{3}-6ay^{2}+12ay-8a\right)
Factor out 2.
a\left(y^{3}-6y^{2}+12y-8\right)
Consider ay^{3}-6ay^{2}+12ay-8a. Factor out a.
\left(y-2\right)^{3}
Consider y^{3}-6y^{2}+12y-8. Use the binomial cube formula, p^{3}-3p^{2}q+3pq^{2}-q^{3}=\left(p-q\right)^{3}, where p=y and q=2.
2a\left(y-2\right)^{3}
Rewrite the complete factored expression.