In how many ways a cube can be painted using seven different colors in such a way that no two faces are in same color?

$ 
\textbf{(A)}\ 154
\qquad\textbf{(B)}\ 203
\qquad\textbf{(C)}\ 210
\qquad\textbf{(D)}\ 240
\qquad\textbf{(E)}\ \text{None of the above}
$
1. **Calculate the total number of ways to paint the cube without considering symmetry:**
   - There are 7 different colors available.
   - We need to paint 6 faces of the cube such that no two faces have the same color.
   - The number of ways to choose colors for the 6 faces from 7 colors is given by the permutation of 7 colors taken 6 at a time:
     \[
     7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 = 5040
     \]

2. **Account for the symmetries of the cube:**
   - A cube has 24 symmetries. This can be understood as follows:
     - Any of the 6 faces can be chosen to be on top.
     - For each choice of the top face, the cube can be rotated around the vertical axis in 4 different ways.
     - Therefore, the total number of symmetries is:
       \[
       6 \times 4 = 24
       \]

3. **Divide the total number of ways by the number of symmetries to avoid overcounting:**
   - Since each distinct coloring can be rotated into 24 different orientations that look the same, we divide the total number of ways by 24:
     \[
     \frac{5040}{24} = 210
     \]

4. **Conclusion:**
   - The number of distinct ways to paint the cube using seven different colors such that no two faces are the same color is:
     \[
     \boxed{210}
     \]