8.2. Find the value of the expression $a^{3}+12 a b+b^{3}$, given that $a+b=4$.
Answer: 64.

Solution. $a^{3}+12 a b+b^{3}=a^{3}+b^{3}+12 a b=(a+b)\left(a^{2}-a b+b^{2}\right)+12 a b=4 a^{2}-4 a b+4 b^{2}+12 a b=4(a+b)^{2}=64$.