2. (15 points) Let $x_{1}, x_{2}, \cdots, x_{2008}$ be integers, and satisfy the following conditions:
(1) $-1 \leqslant x_{n} \leqslant 2 \quad (n=1,2, \cdots, 2008)$;
(2) $x_{1}+x_{2}+\cdots+x_{2008}=200$;
(3) $x_{1}^{2}+x_{2}^{2}+\cdots+x_{2008}^{2}=2008$.
Find the minimum and maximum values of $x_{1}^{3}+x_{2}^{3}+\cdots+x_{2008}^{3}$.
2. Let $x_{1}, x_{2}, \cdots, x_{2008}$ have $q$ zeros, $r$ negative ones, $s$ ones, and $t$ twos. Then
$$
\left\{\begin{array}{l}
-r+s+2 t=200, \\
r+s+4 t=2008 .
\end{array}\right.
$$

Adding the two equations gives $s+3 t=1104$.
Hence $0 \leqslant t \leqslant 368$.
$$
\begin{array}{l}
\text { By } x_{1}^{3}+x_{2}^{3}+\cdots+x_{2008}^{3}=-r+s+8 t \\
=6 t+200,
\end{array}
$$

we get $200 \leqslant x_{1}^{3}+x_{2}^{3}+\cdots+x_{2008}^{3}$
$$
\leqslant 6 \times 368+200=2408 \text {. }
$$

From the system of equations (1), we know:
When $t=0, s=1104, r=904$, $x_{1}^{3}+x_{2}^{3}+\cdots+$ $x_{2008}^{3}$ takes the minimum value 200;
$$
\text { When } t=368, s=0, r=536 \text {, } x_{1}^{3}+x_{2}^{3}+\cdots+
$$
$x_{2008}^{3}$ takes the maximum value 2408.