Open file via SSH and Sudo with Emacs

I want to open a file inside Emacs which is located on a remote server, with sudo powers on the server. I can open local files with sudo via Tramp like this:

C-x C-f /sudo::/home/user/file

But I want to use sudo on the server:

C-x C-f /sudo::user@server/home/user/file

But this gives me sudo powers on my local machine, it asks for my sudo password on the local machine. Is there a way to use sudo on the server?

BTW: Emacs is not installed on the server