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\frac{y^{3}-8-6y^{2}+12y}{8}
Factor out \frac{1}{8}.
\left(y-2\right)^{3}
Consider y^{3}-8-6y^{2}+12y. Use the binomial cube formula, a^{3}-3a^{2}b+3ab^{2}-b^{3}=\left(a-b\right)^{3}, where a=y and b=2.
\frac{\left(y-2\right)^{3}}{8}
Rewrite the complete factored expression.