Here’s how to embed a YouTube Playlist without resorting to a third-party plugin (e.g. WordPress plugin):

Step 1: Find the playlist you want to embed, and grab the playlist ID from the URL.

Step 2: Add the ID to the following embed code:

<iframe width="560" height="315" src="https://www.youtube.com/embed/videoseries?list=PLAYLIST_ID_GOES_HERE" frameborder="0" allow="autoplay; encrypted-media" allowfullscreen></iframe>

Reference: YouTube Help – Embed videos & playlists