Going out on a limb here and guessing that the function is
[tex]f(x)=8x^2\tan^{-1}(7x^3)[/tex]
Please correct me if this isn't the case.
Recall that
[tex]\tan^{-1}x=\displaystyle\sum_{n\ge0}\frac{(-1)^nx^{2n+1}}{2n+1}[/tex]
which converges for [tex]|x|<1[/tex].
It follows that
[tex]8x^2\tan^{-1}(7x^3)=8x^2\displaystyle\sum_{n\ge0}\frac{(-1)^n(7x^3)^{2n+1}}{2n+1}[/tex]
[tex]=\displaystyle\sum_{n\ge0}\frac{56(-49)^nx^{6n+3}}{2n+1}[/tex]
