Yes there are several ways it can be done although bare in mind it's probably illegal. :shame:
The easiest way would be to use one of the many youtube to MP3 converter websites such as this one: http://www.youtube-mp3.org
Another option would be to use a specific software program which can make WAV audio recordings direct from either the computers audio driver (allowing for lossless audio quality) or from the Windows audio driver (minuscule loss in quality but would allow for more flexibility). These allow you to record absolutely any audio from your computer including YouTube, Spotify, TV websites or any digital or analogue audio inputs into your computer. An example of this type of software is Replay Music from Applian.
Depending on what make of motherboard/sound card you have you may even have a free audio recording program included with your audio driver. If you ever update your audio driver by downloading the proper drivers from your motherboards/sound cards website it's worth checking to see if there's a free audio recording programme bundled in with it. Not all audio drivers include recording software but IME most of the good quality ones do.