Can You Play Black on Xbox 360? No - Only PS2 & PC, Plus Similar Xbox 360 Shooters

No. Black (2006) was released only for PlayStation 2 and PC. It never received an Xbox or Xbox 360 port, nor is it backward‑compatible on modern Xbox consoles.

If you want a similar high‑octane, destructive shooter on Xbox 360, consider Blacksite: Area 51, The Club, or the Call of Duty series.