Formula use:
a^3-b^3=\left(a-b\right)^3+3.a.b\left(a-b\right)
Explanation
Here, given expression is :
x^3-\large\frac{1}{x^3}
\rightarrow\left(x\right)^3-\left(\large\frac{1}{x}\normalsize\right)^3
\rightarrow\{\left(x-\large\frac{1}{x}\right)^3\normalsize+3.x.\frac{1}{x}\left(x-\large\frac{1}{x}\normalsize\right)\}
According to the question : x-\large\frac{1}{x}\normalsize = p
\therefore\{\left(p\right)^3+3\times1\times p\}
\therefore p^3+3p
Ans: p^3+3p.