Electric potential of a cube of 8 point charges

[grantaere]

Homework Statement

Find the Electrostatic potential energy of a cubical configuration of point charges. (One charge on each corner of a cube). Each of the charges is 3.00e and the edge of the cube is 3 cm.

Homework Equations

U = kqQ/r

The Attempt at a Solution

I'm pretty sure I understand the conceptual idea of how to do this-- add up the potential energy contributions from the addition of each charge one at a time. However, this seems extremely time-consuming and I'm not sure how to simplify the process like a hint on the question specifies.
Hint given: "The potential energy of a charge in a field is the product of the charge and the potential at its location. Try to make use of symmetry to simplify your work. Look up the tables for the meaning of esu."
Thanks in advance!

 

[Orodruin]

Try to write it all as a sum over each individual pair of charges. What you then need to do is to consider (by symmetry arguments) how many pairs there are of each distance (for example, there are four pairs separated by the maximal distance $\sqrt{3} a$, where $a$ is the cube side length.