Air Carrier A320 flight crew reported a fumes event during boarding. After a maintenance engine run it was determine that the fumes were caused by an external environmental source and not the aircraft. Aircraft departed safely.

Narrative

During boarding at ZZZ; we smelled a level 2; musty odor from the aircraft environmental system. The odor was detected in the cockpit; forward galley and mid cabin by both pilots; the F2; a deadheading Captain; and several customers. The aircraft configuration was APU on; APU bleed on; [and] packs on. Using the FCOM (Flight Crew Operations Manual) odor isolation; we shut down the APU; but the odor continued to linger. We deplaned the aircraft and contacted MX (Maintenance) Control. MX Control stated the aircraft had a history of APU odor events and they believed that was the source of the odor. They asked if we would do an engine run without using the APU; to see if we could isolate the odor. Under the direction of contract maintenance; we conducted an engine run with no evidence of odor from the packs. Maintenance control returned the aircraft to service.The F2 reported symptoms (head ache) and stated she smelled the odor on the previous descent. The F2 contacted MedLink; and they advised that she could operate the flight to ZZZ1 if her symptoms dissipated and MX Control returned the aircraft to service.After the engine run; the F1; F3; and F4 returned to the aircraft in preparation for boarding. When they walked on; they reported that they detected a strong odor on the jet bridge and forward galley. After much deliberation with the FA's (Flight Attendant); Dispatch and Maintenance Control; we determined that an external environmental source was the cause of the FA's new odor event. The likely source was the external high pressure air cart which was running in close proximity to the jet bridge. With the F2 medically cleared; the aircraft returned to service; and the source of the new odor resolved; we reboarded the aircraft and departed uneventfully to ZZZ1.