Communication between arduinos over 4 interchangeable pins

Thank you, that makes sense.

With the cubes, I would do it in an other way.
I would use two diodes per pin (642=48 diodes per cube, perhaps only 12 is enough) to power the cubes, and have the datastream on top of the power. I would use a high frequency (100kHz or more) and multi-master-slave configuration. Like the network for the 433MHz (I forgot the name). You would only need two wires with that.
With the high frequency, it is easier to seperate it from the power lines.

You could also have a capacitance coupling. Make the inside of the walls of the cube with copper, and perhaps it is possible to communicate with the next cube.

I'm curious about other ideas, now that we know what it is for.