Solution:

The electric potential \( V \) at the center of the cube due to a point charge \( q \) is:
\[
V = \frac{kq}{r},
\]
where \( r \) is the distance of the charge from the center.

1. Distance from center:
For a cube of side \( b \), the distance of any vertex from the center is:
\[
r = \frac{\sqrt{3}b}{2}.
\]

2. Potential due to 7 charges:
Since potential is scalar, the total potential is the sum of potentials due to all charges:
\[
V_{\text{total}} = 7 \cdot \frac{kq}{r}.
\]

Substitute \( r = \frac{\sqrt{3}b}{2} \):
\[
V_{\text{total}} = 7 \cdot \frac{kq}{\frac{\sqrt{3}b}{2}} = 7 \cdot \frac{2kq}{\sqrt{3}b} = \frac{14kq}{\sqrt{3}b}.
\]

Thus, the potential at the center is \(\frac{14kq}{\sqrt{3}b}\).