Black Square is a passenger relaxing onboard the Space Symphony ship in Space Channel 5 Part 2. In Extra Report 1, he's just one of many people shown "how to boogie" by the Robos under Shadow's orders. Ulala must save him from being teleported away with the Rescue Beam when he's revealed.
“Former Space Civil Servant leading a comfortable life thanks to his hefty savings. He enjoys nothing better than a good space muffin along with some galactic tea at the Open Café.”