If xy(x + y) = m, then the value of x3 + y3 + 3m is?

Answer: Option C

$$\begin{array}{rl}& xy\left(x+y\right)=m\\ & \text{find }{x}^3+y^3+3m\\ & xy\left(x+y\right)=m.....(i)\\ & \left(x+y\right)=\frac{m}{xy}\\ & \text{Cubing both side}\\ & \Rightarrow x^3+y^3+3.xy\left(x+y\right)=\frac{m^3}{x^3{y}^3}\\ & \text{From equation (i)}\\ & \Rightarrow x^3+y^3+3.m=\frac{m^3}{x^3{y}^3}\\ & \Rightarrow x^3+y^3+3m=\frac{m^3}{x^3{y}^3}\end{array}$$