score:3
1572, with the capture and execution of TΓΊpac Amaru, the last Inca monarch.
TΓΊpac Amaru's execution effectively completed the Spanish conquest of the Inca Empire that had started 40 years earlier with the Battle of Cajamarca (November 16, 1532) and the capture of Atahualpa.
Upvote:4
Take your pick from the following:
16 November 1532: Pizarro captures the Inca Atahulpa at Cajamarca.
26 July 1533: Pizarro executes the Inca Atahualpa at Cajamarca.
15 November 1533: Pizarro seizes the city of Cuzco.
July 1537: Manco Inca abandons his rebellion against the Spaniards and retreats to Vilcabamba.
September 1572: The Spaniards execute the last Inca, Tupac Amaru, in Cuzco.
I don't think there's one particular year in which you could say the conquest of the Incas occurred (just as you can't say that the defeat of the Germans in WWI or WWII occurred in one particular year).
I would say that November 1532 (Atahualpa's capture) was the beginning of the end, and that September 1572 (Tupac Amaru's execution) was the end of the end.