This app was mentioned in 6 comments, with an average of 1.17 upvotes
You could also use this app. It can only download songs which have this option enabled, but this track does.
I also included a Dropbox link to a higher quality download in another comment here.
https://play.google.com/store/apps/details?id=com.gruebeltech.soundloaderpro&hl=en
For Android users only.
It will only let you download only verified songs with the google play version, but if you look through the options it will give you links to other app stores, and those versions will allow you to download any song you like. It also includes tag editing before the download, and will download and embed any album art as well.
Over 1 million downloads and so many people on reddit haven't heard of it. Download it quick before it is taken down:
Soundloader: SoundCloud downloader
Edit: Providing an app to directly download files from SoundCloud instead of making a huge workaround, fuck me right?
If you are willing to root, you could download music on your phone with Google music and then use the app called Play Music Exporter to extract that music to a specified folder. Or, you could use SoundCloud and then Soundloader to download the wanted music so you could use Poweramp to listen to it
SoundLoader for SoundCloud by gruebelTech on the Google Play store
https://play.google.com/store/apps/details?id=com.gruebeltech.soundloaderpro