The Sumerian city-states rose to power during the prehistoric Ubaid and Uruk periods. Sumerian written history reaches back to the 27th century BC and before, but the historical record remains obscure until the Early Dynastic III period, c. the 23rd century BC, when a now deciphered syllabary writing system was developed, which has allowed archaeologists to read contemporary records and inscriptions. Classical Sumer ends with the rise of the Akkadian Empire in the 23rd century BC. Following the Gutian period, there is a brief Sumerian Renaissance in the 21st century BC, cut short in the 20th century BC by Semitic Amorite invasions. The Amorite "dynasty of Isin" persisted until c. 1700 BC, when Mesopotamia was united under Babylonian rule. The Sumerians were eventually absorbed into the Akkadian (Assyro-Babylonian) population.
Is there an answer to this question (If it cannot be answered, say "unanswerable"): When does Classical Sumer end?
rise of the Akkadian Empire