A cubic function $f(x)$ with leading coefficient 1 satisfies the following condition.
For the function $f(x)$,
$$f(k-1)f(k+1) < 0$$
has no integer solutions for $k$.
If $f'\left(-\frac{1}{4}\right) = -\frac{1}{4}$ and $f'\left(\frac{1}{4}\right) < 0$, find the value of $f(8)$. [4 points]