B757 Captain reported aircraft handling problems due to incorrect loading of cargo resulting in the aircraft operating outside of weight and balance guidelines. The flight crew was notified of the issue after takeoff; and obtained corrected performance data.

Narrative

Crew received an ACARS from Dispatch that the airplane W&B (Weight and Balance) was not calculated correctly. Dispatch told the flight crew that 4 cans that were calculated as full of freight; were in fact empty. This produced a 14;000 [pound] weight discrepancy and a center of gravity issue. As the flying pilot; I noted on takeoff that the airplane was extremely nose heavy when I tried to rotate; but we had not received this information yet. When queried by Dispatch about abnormal aircraft handling characteristics; we replied we did see/feel them. Dispatch then came back with the correct weight and balance information for us and sent it to the airplane. We attempted to use the performance software; but we are unable to change any weight or CG numbers in there manually. We reverted to aircraft EFB to get correct landing data. The rest of the flight was uneventful and we landed at the scheduled airport. We did not declare an emergency. We were unaware that the airplane was outside of the flight envelope until well after landing.Cause: I'm operating [on] assumptions here; but I believe a communication breakdown occurred between the aircraft handlers and the ramp agent. It may [have] been earlier than that with the folks that load the cans with freight and the W&B planner for the flight.Suggestion: Secure the software that Boeing has so the aircraft thinks it knows its own weight as a triple check to the process.