Can we cook on the 1st Day of Sukkot (the Feast of Sukkahs/Tabernacles/Booths) and the 8th Last Great Day at the end of that feast?

Answer From The Annual Reading Schedule - Week 28 Notes For Leviticus: No. In Leviticus 23:39 we are told to have a "Shabbatown" (rest) on the 1st Day of Sukkot (Feast of Sukkahs/Tabernacles/Booths) and on the 8th Last Great Day. In Leviticus 23:35-36, we are told also to have a Set-Apart Gathering and Reading on these days – so these days are also, like Yom Teruah (the 1st Day of the 7th Biblical Month), Set-Apart. The 1st and 8th Days at the beginning and end of the Feast of Tabernacles (Sukkot) are Set-Apart Days on which we should have a Shabbatown, and therefore the same answer as given for the 1st Day of the 7th Biblical Month (Yom Teruah) applies for these days as well. Please see the answer for the question about the 1st Day of the 7th Biblical Month (Yom Teruah) for more details.