If you want to stream your entire MP3 music collection or your playlists from a computer or a network media drive to your Amazon FireCube then you can via MusicStreamer. Simply download the app, scan your network and pair to your FireCube.
Amazon Fire Sticks are currently unsupported by MusicStreamer.
In MusicStreamer your FireCube should already be selected as the playback device. If it isn't, simply tap the AirPlay icon to the right of the volume slider and select your FireCube from the list.