Under Basic cPanel/WHM Configuration on your dedicated server or VPS, there is an area called Primary Interface. By default, if this isn't filled in, it will use eth0 (which isn't always correct).
In order to find out which interface is the correct primary interface, please SSH into your server and run:
You can tell which one is the primary by the one having your public IP address on it. Set the Alternate Main Ethernet Device under the Basic cPanel/WHM Configuration to the correct interface. For example: eth1. Then hit "Okay".
Restarting cPanel should not be necessary however it is recommended. To do so, simply login to SSH and run the following:
service cpanel restart