Is God of War 3 Coming to Xbox 360? No.

God of War III (2010) is and will remain a PlayStation 3 exclusive. Developed by Santa Monica Studio, published by Sony Interactive Entertainment. Never ported, announced, or hinted for Xbox 360.

Sony's first-party strategy relies on exclusives to drive hardware sales. God of War is a flagship franchise — moving it to a competitor's platform would undermine their entire ecosystem. The game was built specifically for PS3's Cell architecture; a port would require near-total rewrite.

If you want to play it today: PS3 (disc/digital), PS Now (streaming), or God of War III Remastered on PS4 (included in God of War Saga / PS Plus Premium).