"Admin" user automatically has sudo privileges
Solution 1:
By default adduser adds every new user to a group with the same name as the user's (the group is created if it doesn't already exists). So if you create a user called admin it will be added to the group admin.
/etc/sudoers contains the line
%admin ALL=(ALL) ALL
which means that all members of the group admin are allowed to use sudo - and that's true for your admin user, too.