Downloading Music to Xbox 360: Not Directly Possible

You cannot download music directly to Xbox 360 via the Xbox Store—no native music download function exists.

Alternatives for Music on Xbox 360:

• Streaming Apps: Download Spotify, Amazon Music, Pandora apps from Xbox 360 Store (Xbox Music discontinued).
• USB Drive: Play MP3/WMA files from USB (format support limited).
• Media Server: Stream from PC/NAS via Plex, Windows Media Player sharing.
• In-Game Soundtracks: Some games allow custom music import.

Xbox 360 is a gaming console first; music playback is secondary.