If a + 1/a = 3, then the value of a^3 + 1a^3 is?

Answer: Option D

$$\begin{array}{rl}& \text{Given , }a+\frac{1}{a}=3\\ & \text{Cube both sides}\\ & a^3+\frac{1}{a^3}+3\times a\times \frac{1}{a}\left(a+\frac{1}{a}\right)={\left(3\right)}^3\\ & \Rightarrow a^3+\frac{1}{a^3}+3\times 3=27\\ & \Rightarrow a^3+\frac{1}{a^3}=27-9\\ & \Rightarrow a^3+\frac{1}{a^3}=18\end{array}$$