DA20 Flight Instructor reported engine partial power loss during cruise. Pilot returned to departure airport where engine failed completely upon landing.

Narrative

At ZZZ I conducted the preflight inspection of Aircraft X. I found the aircraft to be in airworthy condition. After completing the preflight inspection; I performed the safety briefing and discussed the plan for the flight with the customer. The customer and myself boarded the aircraft. I conducted the pre-start checklist and then commenced the starting engine checklist. There were no abnormalities observed during the engine start. I completed the pre-taxi checklist and taxied to the run-up area. During the completion of the run-up checklist; everything operated normally. Both magnetos were grounded and both sides dropped 20-30 RPMs. All engine gauges were normal. Upon completion of the run-up checklist; we taxied to runway XX. I completed the before takeoff checklist and taxied out on runway XX. During the takeoff roll; engine gauges were green and airspeed was alive; we lifted off and climbed out with no abnormalities. Upon reaching 400ft AGL; I completed the climb checklist and continued the climb to 1;800 MSL. I tried contacting ZZZ1 Approach; but was blocked by another aircraft so I never made two-way radio contact. I began reducing throttle to cruise RPMs and noticed the engine beginning to lose more power than it should. I put the throttle back in to full; confirmed the mixture was rich and fuel pump on. The engine was then intermittently surging with a reduction in power and then back to normal power. At this point; I decided an immediate return to ZZZ was warranted. I did not declare an emergency with ZZZ1 Approach and instead switched back to the ZZZ CTAF to coordinate my arrival with other aircraft in the area. During the turn back to ZZZ; I experienced partial power loss; with the engine no longer surging. I tried adjusting the mixture and then back to full rich; turned on the fuel prime; and adjusted the throttle once more and with no success. As I approached the airport; and knew I was within gliding distance; I tried cycling the magnetos to both left and right; which did not help and could feel the engine power decreasing more; so I cycled back to both. As I turned base; I felt the engine lose all power. The prop was still spinning at this point with the airspeed. Turning final; I slowed the airspeed and deployed the flaps to the landing configuration; conducted a forward slip and made a normal landing on runway XX. The prop quit spinning shortly before touchdown. We were able to roll down runway XX and turn onto taxiway 1 and clear runway XX with the aircraft's residual momentum. Upon coming to a stop; I secured the aircraft and we evacuated the plane safely.