C-182 pilot reported a near miss while in the airport traffic pattern on approach.

Narrative

I am a student at a flight school. I was flying a Cessna 182 to get my 3 night currency landings at ZZZ. I flew one pattern; landed; took off again; and the issue occurred on my second lap. While I was right mid-field downwind for Runway XXR; I was cleared to land #3. While I thought I had the two targets in front of me in sight; I was wrong and only had one. I ended up cutting off who was supposed to be #2 to land. In the dark; there is an extreme amount of lights. With multiple runways; parallel runways; it being a large airport; the nearby area being lit up with white and red lights; lots of busy roads with stoplights and car lights right below; multiple flight schools training in the area; etc; it was very easy to lose an airplane in the dark. When I was on final I heard the #2 aircraft tell Tower they were going around. At the same time; I saw the them above me going around. I continued my approach and landing; as I figured it was the safest. I was wrong in the fact that I cut off the traffic ahead of me; and I understand and will be sure to clarify and verify where the traffic is in the future. What concerns me is what the Tower was doing during this time. While I understand they are task saturated; so are we as pilots. I was cleared to land #3 on the downwind at night at a large airport with parallel runways and was able to fly my downwind; cut off the traffic on base (I think; I am not positive of the flight paths) and continue to fly the final leg before the pilot of the other aircraft spotted me and went around. I would expect ATC to catch the mistake before any of the pilots did; and that is what concerns me.