Air carrier Captain reported 'strong dirty socks' odor during preflight. After extensive maintenance troubleshooting the flight was canceled.

Narrative

Upon arrival to our aircraft at the gate in ZZZ the whole crew notice a very strong dirty sock smell in the entire Cabin. The odor was so strong that inflight was unable to come in the aircraft an perform their preflight duties. Me and the first officers went in the aircraft and quickly open the cockpit windows; we communicated with ground ops to open all doors of the aircraft in order to remove the odor. I noticed the bad odor was written up in prior to arriving at ZZZ. I informed maintenance and they decided to MEL the APU. Finally the odor was removed; we boarded our customers and proceeded with our push back and engine start up with the air start procedures. After we started the first engine a few minutes past and I received I call from [the flight attendants] stating the smell was back again. I informed them to let's start the second engine and see if it were to go away. We started the second engine and I received a call again stating the smell was worst than before. At that point with communication with dispatch and maintenance we decided to return to the gate. At that point we deplaned the customers. On maintenance request we ran the engine with pack 2 on individually and the odor returned; we then ran pack 1 individually and the odor returned even worst. At that point maintenance decided this was not able to continue.