It has its own Song in the Temple Service: Rosh HaShanah 4b; Succah 47a, 48a
It has its own Additional Offering, unlike the order of the rest of Succot: Rosh HaShanah 4b; Succah 47a, 48a
How much water is used for the Water Libation in the Temple: Succah 47a, 48b
The bringing of a Bull for the Additional Offering necessitates its own lottery for the Kohanim to partake, instead of joining in the order of the rest of Succot: Rosh HaShanah 4b; Succah 48a, 55b
Which shifts of Kohanim are eligible for the above Lottery: Succah 55b
Considering the additional offering of the 8th Day to be representative of the Jewish people, where those of the rest of Succot represented the nations of the World: Succah 55b