How to change the sudo password?

Is there a way to change the sudo password after installation has taken place? I know you can change the user password via that box in ‘About me’ but that still leaves behind the old sudo password.

Here it is:

su -c 'passwd root'

enter the “old” password to execute the command to change the password, then enter the new password twice when asked for, done.

What you call the “sudo password” is the password of the user *root. *Thus the user root should change his password. For that he needs to execute the chpasswd command. You can do that is the way you are used to execute commands as root (possible using sudo).