Let us go now to I Kings 8:65-66. Again the Feast of Tabernacles shows 7 days long. This one shows the order of events just a little bit more clearly. Same general story, same time element.
The order of events was they had the dedication of the altar, and then they held the Feast for seven days. That was a total of fourteen days, and then he sent the people home on the 23rd. By that time, the 23rd, the eighth day was over too.