Solution
Ports that must be open to run cPanel behind a firewall:
port service protocol direction
20 ftp tcp inbound/outbound
21 ftp tcp,udp inbound/outbound
22 ssh tcp inbound
25 smtp tcp inbound/outbound
26 smtp tcp inbound/outbound
37 rdate tcp outbound
43 whois tcp outbound
53 DNS tcp/udp inbound/outbound
(inbound is only needed if you run your own public DNS server you)
80 http tcp inbound/outbound
110 pop3 tcp inbound
113 ident tcp outbound
143 imap4 tcp inbound
443 https tcp inbound
465 smtp tls/ssl tcp/udp inbound/outbound
873 rsync tcp/udp outbound
993 imap4 ssl tcp inbound
995 pop3 ssl tcp inbound
2082 cpanel tcp inbound
2083 cpanel ssl tcp inbound
2086 whm tcp inbound
2087 whm ssl tcp inbound
2089 cp licence tcp outbound
2095 Webmail tcp inbound
2096 Webmail SSL tcp inbound
3306 mysql tcp (only if you need to connect remotely)
6666 chat tcp inbound