YouTube videos are downloadable in the YouTube app, but not on your phone storage directly. Downloaded videos available on your YouTube app until you delete them, but YouTube requires that you go online once every 30 days. So, if you have a working internet connection even once in 29 days, you can have the offline videos forever.
If you want to download speech or any other on your phone, there are some apps that allow you to download YouTube videos directly on your phone storage.
Best YouTube video downloading apps:
3) TubeMate 2
8) YT3 YouTube Downloader
10) Media Clip Pro Video Downloader
Where it is available:
Videoder - available on play store or get it from videoder.com.
TubeMate - get it on tubemate.net.
TubeMate 2 - search the app and get it on softonic.com.
Snaptube - get it on snaptubeapp.com.
KeepVid - get it on keepvid.com.
Ins tube - get it on instube.com.
Vidmate - get it on vidmateapp.com.
YT3 YouTube downloader - get it on yt3dl.net.
YMusic - Get it on ymusic.io.
Media Clip Pro video downloader - Search the app and get it on apkpure.com.
Download any one of these apps by user ratings and the app guides you to download the YouTube video.
How to download YouTube video without any app:
If you are using a browser to play YouTube videos, it is very easy to download within a minute.
If you wish to download the YouTube video, when it is playing on a browser, click the video link and add the word "magic" between "you" and "tube" as "www.youmagictube.com/..." and enter it to go to the website, fetchtube.com. Here you can select "Load options" and it displays to select the quality of your video like 460p, 360p, etc. Then click any one of the video quality to download. It will directly download the video on your browser.
Or simply copy the YouTube video link and paste the link on fetchtube.com to download.