Electrostatic potential is a harmonic function on any region without charges. It has no local minimum, in fact the value at the origin is the average of the potential over a sphere centred at the origin within your "cage".  Therefore it is impossible to do what you want: there will always be a path the electron can take to escape to infinity.

EDIT:
Just for fun, I tried it numerically using $60$ unit charges at the vertices of a truncated icosahedron, with $100$ randomly chosen initial velocities with speed $0.01$.  By time $t=40$, all but four had managed to escape the cage.    An animation of the trajectories is [here](http://www.math.ubc.ca/~israel/problems/spherescape.gif).