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y=\left(512x^{3}+960x^{2}+600x+125\right)\left(x^{3}+3\right)
Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(8x+5\right)^{3}.
y=512x^{6}+1661x^{3}+960x^{5}+2880x^{2}+600x^{4}+1800x+375
Use the distributive property to multiply 512x^{3}+960x^{2}+600x+125 by x^{3}+3 and combine like terms.