Answer: Option C
$$\eqalign{
& xy\left( {x + y} \right) = m \cr
& {\text{find }}{x^3} + {y^3} + 3m \cr
& xy\left( {x + y} \right) = m\, . . . . . (i) \cr
& \left( {x + y} \right) = \frac{m}{xy} \cr
&{\text{Cubing both side}} \cr
& \Rightarrow {x^3} + {y^3} + 3.xy\left( {x + y} \right) = \frac{{{m^3}}}{{{x^3}{y^3}}} \cr
& {\text{From equation (i)}} \cr
& \Rightarrow {x^3} + {y^3} + 3.m = \frac{{{m^3}}}{{{x^3}{y^3}}} \cr
& \Rightarrow {x^3} + {y^3} + 3m = \frac{{{m^3}}}{{{x^3}{y^3}}} \cr} $$