2.156. Calculate the sum of the cubes of two numbers if their sum and product are 11 and 21, respectively.
Solution.

Let $a+b=11$ and $a b=21$. Then

$$
\begin{aligned}
& a^{3}+b^{3}=(a+b)\left(a^{2}-a b+b^{2}\right)=(a+b)\left((a+b)^{2}-3 a b\right)=11\left(11^{2}-3 \cdot 21\right)= \\
& =11(121-63)=638
\end{aligned}
$$

Answer: 638.