Each edge of a cube is increased by $50 \%$.  The percent of increase of the surface area of the cube is:
$ \textbf{(A)}\ 50 \qquad\textbf{(B)}\ 125\qquad\textbf{(C)}\ 150\qquad\textbf{(D)}\ 300\qquad\textbf{(E)}\ 750 $
1. Let the original edge length of the cube be \( x \). The surface area \( A \) of a cube with edge length \( x \) is given by:
   \[
   A = 6x^2
   \]

2. When the edge length is increased by \( 50\% \), the new edge length becomes:
   \[
   1.5x
   \]

3. The new surface area \( A' \) of the cube with the new edge length \( 1.5x \) is:
   \[
   A' = 6(1.5x)^2
   \]

4. Calculate \( (1.5x)^2 \):
   \[
   (1.5x)^2 = 1.5^2 \cdot x^2 = 2.25x^2
   \]

5. Substitute \( 2.25x^2 \) back into the expression for the new surface area:
   \[
   A' = 6 \cdot 2.25x^2 = 13.5x^2
   \]

6. The increase in surface area is:
   \[
   \Delta A = A' - A = 13.5x^2 - 6x^2 = 7.5x^2
   \]

7. The percent increase in surface area is given by:
   \[
   \text{Percent Increase} = \left( \frac{\Delta A}{A} \right) \times 100 = \left( \frac{7.5x^2}{6x^2} \right) \times 100
   \]

8. Simplify the fraction:
   \[
   \frac{7.5x^2}{6x^2} = \frac{7.5}{6} = 1.25
   \]

9. Multiply by 100 to get the percentage:
   \[
   1.25 \times 100 = 125\%
   \]

Conclusion:
\[
\boxed{125}
\]