I have a site, and I buy a VPS for its running. This VPS contain several cpanels. and I give one cpanel for someone's site, so I should give the password of the VPS to this person. I want to inquire if it is safe for my site's database? , can he download my site's database with any way? I'm so worried about it.
Taking on a VPS is equivalent to a dedicated server when it comes to administration. Either purchase a properly managed VPS or get someone to help you. If you have no experience of securing and administrating servers connected to the internet you need to get help to start with.
I can tell you about the hosting provider: An encrypted file system on a VPS provides no additional security if you are worried about your hosting provider snooping. They can just capture your password when you enter it for decryption. Also, if your VPS is running the encrypted file system would be unlocked and everything would be readable. In general, you should assume your VPS provider has access to everything. If they have root on the host machine they will be able to get root access to the VPS. You do have options though. As others have mentioned, encrypting the data before backing it up to the VPS would work. Using GPG locally is the answer. You must be careful never to decrypt on the actual VPS though.