According to the official tutorial, there are 2 methods to download SoundCloud music - one for computer, and the other for mobile devices.
For users who access SoundCloud through computers, it may not be possible to download all the songs you like, because some songs don't have download links. For downloadable songs, find the "More" option as shown in the picture below and click the "Download file" button.
Only mobile users with SoundCloud Go or SoundCloud GO+ subscription are able to download offline music files to their devices. Users with free accounts can only listen to streaming music on their mobile devices.