Simply adding a password for root is not enough for Ubuntu 14.04 Server.

You also need to edit /etc/ssh/sshd_config, and comment out the following line:

PermitRootLogin without-password

Just below it, add the following line:

PermitRootLogin yes

You need to setup a password for the root account and then it will work.

sudo passwd

Enter same password twice.

P.S. After modifying /etc/ssh/sshd_config don’t forget to reload the openssh server.

sudo service ssh reload

Then restart SSH:

service ssh restart