In order for you to manage your domains in cPanel/WHM you cannot use the DigitalOcean DNS servers. cPanel/WHM includes a fully functional and integrated DNS server of it's own. Instead what you'll want to do:
1.) It is recommended to have a secondary DNS server, your cPanel/WHM server can act as your primary and cPanel offers free DNS-Only licenses for a lightweight version for use on your secondary server(s).
Note: while it's not recommended, some registrars may allow you to create your two nameservers with the same IP address. It may also be possible (I have not tested this) to use your main ipv4 address and a floating IP for the same effect.
2.) With your domain registar, GoDaddy in this case, you will want to register new nameservers by creating nameserver glue records. You'll create an ns1.yourdomain.com and ns2.yourdomain.com and point them to your droplet's IP addresses.
Now once the new registrations propagate (this could take up to 24-48 hours but is often quicker), you will be able to create domains and sites directly in cPanel/WHM after pointing the domain(s) to ns1.yourdomain.com/ns2.yourdomain.com