The external factors that led to the collapse of the Aztec Empire were centered on the abilities of the Spaniards, the germs they carried with them, and the enmity of the Aztecs’ subject peoples.
The Spaniards had, in Jared Diamond’s phrase, “guns, germs, and steel.” These external factors made it very hard for the Aztecs to stand against them. The germs (smallpox in particular) killed large numbers of Aztecs, weakening the empire. The Spaniards’ steel weapons and armor were qualitatively better than anything the Aztecs had.
Perhaps most importantly, though, the Spaniards had native allies to augment their own small numbers. The Aztecs had made themselves thoroughly hated by the people around them. The Tlaxcalans, in particular, saw the Spanish as a means of getting revenge on the Aztecs. Their help was invaluable to the Spaniards.
In these ways, external factors were the major cause of the collapse of the Aztec Empire.