Come on, now. You know the expectations. Make your best effort to analyze the circuit. Hook up a voltage source between A and B and figure out how much current flows. Once you have done that, then we can consider some alternative ways of viewing the problem so as to exploit symmetry.
@ Teszla: Once you've solved the original problem you should be able to deduce the resistance between any two nodes on the cube. Symmetry is definitely your friend.
this problem is so common that the solution is readily available in the web.. hints: color code and short.. --hope this helps
I tried naming each node a variable letter and then using KCL and got that the voltage Va can be expressed as 3Va = Vc+Vd+Vf (C, D & F being the nodes connecting to A), in the same way Vb can be expressed as 3Vb = Ve+Vg+Vh (E,G & H being the other 3 nodes connecting to B). Is this even a good way to start? Please give me some guiding how to continue.
Why would the voltage on one node, say Node A, be the sum of the voltages on the nodes connected to it? Does that make sense to you? By symmetry, what do you know about Vc, Vd, and Vf relative to each other?