The block could all be powered up prior to starting the game, they check if have no neighbors, run rgd random color assignment, store in eeprom. Then when get powered up in the game, they check to see they have a neighbor, if so read eeprom and turn on their color.
I'm thinking maybe give each face a set of header pins, one horizonal, one vertical, males on 3 faces and females on 3 faces.
Arrange the pins so that they could mount either direction
gnd-vcc-rx-tx-tx-rx-vcc-gnd on the females, then on the males gnd-vcc-tx-rx. The males would go one orientation into the females make the connection, boot up & do its color thing, and then have gnd-vcc-etc, available for the next device.