Air Carrier Captain reported a fume event during initial climb which dissipated and resumed during descent. The flight continued to safe landing at destination where a logbook entry and an aircraft odor form were submitted.

Narrative

After takeoff; during climb; the First Officer noted an odor that he thought might be coming from the forward lavatory. Within a few minutes; the #1 Flight Attendant called. She stated that there was a 'dirty sock' smell in the cabin and that it was 'strong' predominantly in the aft cabin. I asked if the odor was continuing and if it was causing irritation to anyone's eyes; nose or throat. She stated that it seemed to be dissipating and that nobody was feeling any irritation. I called for an update one more time during climb with continued improvement of conditions. Once at cruise; I spoke with the #1 Flight Attendant again and she told me that the smell had abated and everyone was fine. I made a Satcom call to Dispatch and was patched through to Maintenance. I told them of the situation and that I was putting it in the logbook along with an Airbus Cabin Odor Report. The flight continued with no further odor noted in the cabin or in the flight deck. During descent into ZZZ; the #1 called and stated that the odor had returned; although not as bad as before. We did note a light 'dirty sock' odor in the cockpit as well. We landed without incident and had the Station Manager notify contract maintenance.