With the musicbox - audio downloader. You can download audio files (.mp3, .caf, etc.) from an integrated browser and play them on your device on- and offline.

The following features make this app the best in the store:
✓ Bookmarking favorite websites
✓ Creating search bookmarks
✓ Download unlimited audio files
✓ Get ID3 / metadata from the files
✓ Show album artwork
✓ Load artwork from discogs.com
✓ Pausing/resuming downloads
✓ Editing (multiple) audio files
✓ Create unlimited playlists
✓ Search by artist, genre or album
✓ Supports iTunes file sharing (read more below)
✓ Plays audio tracks even when the app is closed.

As mentioned above this app supports iTunes file sharing.
Through iTunes file sharing you can simply add music files to your device through the iTunes environment. This way you can add your own bought music to this app.

The app utilizes the discogs.com API to download artwork