14. There are $(\quad)$ different ways to write 2016 as the sum of a natural number multiple of 2 and a natural number multiple of 3 (for example, $2016=1008 \times 2+0 \times 3=402 \times 2+404 \times 3$).
(A) 236
(B) 336
(C) 337
(D) 403
(E) 672
14. C.

Let $2016=2x+3y(x, y \in \mathbf{N})$. Then $y=\frac{2016-2x}{3}=672-\frac{2x}{3}$.
Since $y \geqslant 0$, we have $0 \leqslant x \leqslant 1008(x \in \mathbf{N})$.
Also, since $y \in \mathbf{N}$, it follows that $2x \equiv 0(\bmod 3)$.
Given $(2,3)=1$, we know $3 \mid x$.
Therefore, there are $\left[\frac{1008}{3}\right]+1=337$ different ways.