If x + y = 7, then the value of x3 + y3 + 21xy is?

Answer: Option C

$$\begin{array}{rl}& x+y=7\\ & \left(\text{cubing both sides}\right)\\ & \Rightarrow {\left(x+y\right)}^3={\left(7\right)}^3\\ & \Rightarrow x^3+y^3+3\left(x+y\right)xy=343\\ & \Rightarrow x^3+y^3+21xy=343\end{array}$$