A two-inch cube $(2\times 2\times 2)$ of silver weighs 3 pounds and is worth \$200.  How much is a three-inch cube of silver worth?

$\textbf{(A)}\ 300\text{ dollars} \qquad \textbf{(B)}\ 375\text{ dollars} \qquad \textbf{(C)}\ 450\text{ dollars} \qquad \textbf{(D)}\ 560\text{ dollars} \qquad \textbf{(E)}\ 675\text{ dollars}$
1. First, calculate the volume of the two-inch cube. The volume \( V \) of a cube with side length \( s \) is given by:
   \[
   V = s^3
   \]
   For a two-inch cube:
   \[
   V = 2^3 = 8 \text{ cubic inches}
   \]

2. We know that this two-inch cube weighs 3 pounds and is worth $200. Therefore, the value per cubic inch of silver can be calculated as:
   \[
   \text{Value per cubic inch} = \frac{200 \text{ dollars}}{8 \text{ cubic inches}} = 25 \text{ dollars per cubic inch}
   \]

3. Next, calculate the volume of the three-inch cube:
   \[
   V = 3^3 = 27 \text{ cubic inches}
   \]

4. To find the value of the three-inch cube, multiply the volume of the three-inch cube by the value per cubic inch:
   \[
   \text{Value of three-inch cube} = 27 \text{ cubic inches} \times 25 \text{ dollars per cubic inch} = 675 \text{ dollars}
   \]

Conclusion:
\[
\boxed{675 \text{ dollars}}
\]