Liked Videos and Liked Music are private playlists, they have a generic URL and you can only access them by being logged in. I have two methods to download Liked Videos:
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Install a desktop app video downloader, most of them have the option to download an entire playlist.
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They also have an option to add a cookies file so you can download private playlists, such as Liked Videos or Watch Later
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Log in to YouTube in your browser
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Export the cookies from the browser
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Import them to the desktop app
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Download Liked Videos
That's what you're supposed to do, however i never got that to work. If it doesn't work, you can transfer all your liked videos from the private playlist to a public playlist. Here's what i do:
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Create a new playlist called Downloads, and make it public; it now has its own specific URL, unlike the generic URL of Liked VIdeos
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Install the YouTube Multiselect browser extention
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Use Multiselect to select every video in Liked Videos and add it to Downloads
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Use the desktop app to download the Downloads playlist
This is how i download my private playlists like Watch Later or Liked Videos, i assume it also works for Liked Music