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8\left(27+d^{3}\right)
Factor out 8.
\left(d+3\right)\left(d^{2}-3d+9\right)
Consider 27+d^{3}. Rewrite 27+d^{3} as d^{3}+3^{3}. The sum of cubes can be factored using the rule: a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right).
8\left(d+3\right)\left(d^{2}-3d+9\right)
Rewrite the complete factored expression. Polynomial d^{2}-3d+9 is not factored since it does not have any rational roots.