7. Let the function $f(x)=x^{3}+a x^{2}+b x+c\left(a, b, c\right.$ all be non-zero integers), if $f(a)=a^{3}, f(b)=b^{3}$, then the value of $c$ is
A. -16
B. -4
C. 4
D. 16
$$
\begin{array}{l}
\Rightarrow a|b \xrightarrow{b=k a} a+k a=-k \Rightarrow k(a+1)=-a \Rightarrow k| a \xrightarrow{a=m k} m k+1=-m \Rightarrow m(k+1)=-1 \\
\Rightarrow m=1, k=-2 \Rightarrow a=-2, b=4 \Rightarrow c=16, \text { so choose } D .
\end{array}
$$