First Temple was built by Solomon in 966BC to 950BC which replaced the Tabernacle constructed in the Sinai Desert Under Moses supervision. First Temple destroyed by the Babylonians in 586 BC(2 Kings 25:8-17). Second Temple Construction was authorized by Cyrus the Great and began in 538 BCE (Ezra 1:1-4) completed in 23 years in 515BC (Ezra 6:15). It is called Zerubbabel’s Temple because the Persian king appointed Zerubbabel as governor of Judah who started rebuilding the Temple with the help of Joshua, the high priest. Zerubbabel was the leader of the tribe of Judah and part of the first Jewish captives.
In the next 400 years, different Non-Jewish rulers built OR defiled the Temple until the 39BC battle in which Herod took charge of the Temple. Herod proposed to renovate the Temple in 20-19 BC. Thus started the third massive reconstruction of the Temple under Herod with an expansion of the Temple Mount. This Temple was famous as Herod’s Temple and was destroyed by Titus in 70AD as Prophesied by Jesus mentioned by Gospel of Matthew and Luke as below:
Matthew 24:1-2: Then Jesus went out and departed from the Temple, and His disciples came up to show Him the buildings of the Temple. And Jesus said to them, “Do you not see all these things? Assuredly, I say to you, not one stone shall be left here upon another, that shall not be thrown down.” NKJV
Luke 21:6: These things which you see—the days will come in which not one stone shall be left upon another that shall not be thrown down. NKJV