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5\left(z^{3}-6z^{2}+12z-8\right)
Factor out 5.
\left(z-2\right)^{3}
Consider z^{3}-6z^{2}+12z-8. Use the binomial cube formula, a^{3}-3a^{2}b+3ab^{2}-b^{3}=\left(a-b\right)^{3}, where a=z and b=2.
5\left(z-2\right)^{3}
Rewrite the complete factored expression.