In order for Mediafast devices to cache and deliver HTTPS content, clients need to have the necessary certificates installed.
To install certificates, navigate to cert.peplink.com, and follow the instructions for your client platform.
You Tube is a different story, they go through great lengths to stop people from downloading or caching their content. You Tube makes their money with advertising, so they lose out when people download or cache their content.
That is the main reason it is currently not possible to download or cache YouTube content.