There are a few ways that you can download iTunes without an administrator password.
One way is to use a third-party software program that will allow you to bypass the password protection on the administrator account.
Another way is to use a bootable USB drive or CD/DVD to access the files on the computer without needing a password. Finally, you can also try resetting the administrator password using a utility such as Ophcrack.
Whichever method you choose, make sure that you have a backup of your important data before proceeding, just in case something goes wrong.