Answer
$49x^6-14x^3+1$
Work Step by Step
Using $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, the given expression, $
(7x^3-1)^2
$, is equivalent to
\begin{array}{l}\require{cancel}
(7x^3)^2+2(7x^3)(-1)+(-1)^2
\\\\=
49x^6-14x^3+1
.\end{array}