correct answer is: d) 234

Formula use: a^3+b^3=\left(a+b\right)^3-3.a.b\left(a+b\right)

Explanation

Here, given expression is :
\left(a^3-\large\frac{1}{a^3}\right)
\rightarrow\{\left(a-\large\frac{1}{a}\right)^3\normalsize+3.a.\large\frac{1}{a}\normalsize\left(a-\large\frac{1}{a}\normalsize\right)\}
According to the question : a-\large\frac{1}{a}\normalsize = 6
\therefore\{\left(6\right)^3+3\times1\times6\}
\rightarrow\left(216+18\right)
\therefore 234
Ans: 234.