Using Copyrighted Songs for a Free Mixtape

Hi, I am currently working on my first ever hip-hop mixtape, which I plan to put only on the Internet completely free. However, for three of the songs, the background beats are tracks from the Metroid Prime video game made by Nintendo in 2002 for Nintendo Gamecube. My plan was to use these songs, more or less unedited, as background beats with my lyrics over them, then use these songs in the mixtape. I just want to make sure if this is legal to do. Nintendo's official website says it cannot give legal advice and that they do not answer requests regarding copyrights and IPs. I would have liked to get some sort of license but it seems that is not possible. So, in short, is it legal to use these songs on my free mixtape, and if not, is there a way for me to get a license so that it is? Thank you.