Question 114
Suppose that $f(x)$ is defined on $\mathbb{R}$, satisfying $f(0) = 2008$, and for any $x \in \mathbb{R}$
$$
\begin{aligned}
f(x+2) - f(x) &\le 3 \times 2^x, \\
f(x+6) - f(x) &\ge 63 \times 2^x.
\end{aligned}
$$
Then $f(2008) = \underline{\hspace{2cm}}$.
$$
\begin{aligned}
f(x+2) - f(x) &\le 3 \times 2^x, \\
f(x+6) - f(x) &\ge 63 \times 2^x.
\end{aligned}
$$
Then $f(2008) = \underline{\hspace{2cm}}$.