Searching for a way to download Xbox 360 RGH system requires understanding that the game was never officially released for that console. It was developed as an exclusive for Why Cuphead isn't on Xbox 360 Platform Exclusivity
Avoid anything labeled as a “repack” of a paid commercial game — especially one never released for that console. Searching for a way to download Xbox 360
While there is no official version, you may encounter several files on sites like Internet Archive or in various "repacks": Xbox One / Series X|S (con Game Pass