If your cPanel server is a shared environment server, your server IP might be blocked by any RBL list such as SpamHaus.
As cPanel by default set the primary email as the SMTP mail IP, to enable different IPs to be send from the cPanel, you may follow the step as below,
1. Log into WHM.
2. Select Service Configuration and choose Exim Configuration Editor.
3. Find “Reference /etc/mailips for outgoing SMTP connections” and enable it.
4. Edit the file named /etc/mailips through SSH.
Replace the host name and IPs with your desired information.