8. Given the function
$$
f(x)=x^{3}-\log _{2}\left(\sqrt{x^{2}+1}-x\right) \text {. }
$$

For any real numbers $a, b (a+b \neq 0)$, the value of $\frac{f(a)+f(b)}{a^{3}+b^{3}}$ is ( ).
(A) always greater than zero
(B) always equal to zero
(C) always less than zero
(D) the sign is uncertain
8. A.
$$
\begin{array}{l}
\text { Since } f(-x)+f(x) \\
=-x^{3}-\log _{2}\left(\sqrt{x^{2}+1}+x\right)+x^{3}-\log _{2}\left(\sqrt{x^{2}+1}-x\right) \\
=0,
\end{array}
$$

Therefore, $f(-x)=-f(x)$, which means $f(x)$ is an odd function.
$$
\begin{array}{l}
\text { Also, } f(x)=x^{3}-\log _{2}\left(\sqrt{x^{2}+1}-x\right) \\
=x^{3}+\log _{2}\left(\sqrt{x^{2}+1}+x\right)
\end{array}
$$

is monotonically increasing on $(0,+\infty)$, so $f(x)$ is an increasing function on $\mathbf{R}$.
Notice that
$$
(f(a)-f(-b))[a-(-b)]>0,
$$

Therefore, $\frac{f(a)+f(b)}{a+b}>0$.
Also, $\left(a^{3}+b^{3}\right)(a+b)>0$, hence
$$
\frac{f(a)+f(b)}{a^{3}+b^{3}}>0 .
$$