1.29 Calculate the sum of the cubes of two numbers if their sum and product are 11 and 21, respectively.
1.29 Let $a$ and $b$ be the required numbers; then $a+b=11$ and $ab=21$. According to formula (1.11), we have $(a+b)^{3}=a^{3}+b^{3}+3ab(a+b)$. Therefore, $a^{3}+b^{3}=(a+b)^{3}-3ab(a+b)$, i.e., $a^{3}+b^{3}=$ $=11^{3}-3 \cdot 21 \cdot 11=638$.

Answer: 638.