can't ping from server to internet

Hello again faziz,

What do your routes look like on the BIG-IP?

Consider the BIG-IP to have basically two networks, one for the "management plane" and one for the "data plane". Given your scenario it sounds like your management plane has a route to the internet (thus traffic from the management network, such as ping, ssh, telnet works) but your data plane does not.

I would not suggest attempting to cross data traffic over to route out of the management network.

If you do a "tmsh show net route" is the gateway reachable via the management port or the external vlan?