mysqladmin won't work

[apost at high-low.net]

"#mysqladmin -u root -h localhost password "mysql"
mysqladmin: connect to server at 'localhost' failed
error: 'Access denied for user: 'root at localhost' (Using password: NO)'

# mysqladmin -h localhost password
mysqladmin: connect to server at 'localhost' failed
error: 'Access denied for user: 'root at localhost' (Using password: NO)'

I don't get it, whats happening?  Btw im using putty to ssh into the
server, could that be a cause?"

==> I'm pretty sure that putty is doing ok. In order to use the mysqladmin commands, you must make a successful authentication with one of the current active accounts. So things should be fine if you would run it like this:
#mysqladmin -u root -h localhost password "mysql" -p

This will prompt you for the old password and after giving that, it should work ok.

Andre