Final answer:
The sack of Rome occurred in 410 CE, and the last Roman emperor was deposed in 476 CE, making it a span of 66 years between these two significant events.
Step-by-step explanation:
The question asks about the time period between the sack of Rome and the abdication of the last Roman emperor. Historically, Rome faced numerous sacks over the centuries, but the traditional date marking the end of the Western Roman Empire is 476 CE. This is when the Germanic chief Odoacer overthrew the last emperor, Romulus Augustulus, and proclaimed himself King of Italy.
Odoacer's rule followed multiple invasions and internal decline, including the sack of Rome by the Visigoths in 410 CE and the subsequent challenges to Roman authority. Thus, from the sack of Rome in 410 CE to the overthrow of the last Western Roman Emperor in 476 CE, there were 66 years. While the Eastern Roman Empire, also known as the Byzantine Empire, continued to exist with its capital in Constantinople until 1453, the western half of the empire with Rome as its cultural center had effectively ceased to exist as an empire.