Why does it say "Kel Hashem"?
Radak: He has all ability, and He is the one who exists 1 .
I.e. His existence is unconditional. Everything else exists only if He wants. (PF)
How did He illuminate for us?
Radak: [He took us out] from Galus, which was dark for us.
Malbim (28): [The Kohanim] came out to greet the king with torches - "Al Ken ba'Urim Kavdu Hashem" (Yeshayah 24:15), so he said to Hashem "va'Ya'er Lanu" - "Ya'er Hashem Panav Elecha" (Bamidbar 6:25)
What do we learn from "Isru Chag ba'Avosim [Ad Karnos ha'Mizbe'ach]"?
Sukah 45a #1: In the Mikdash, on Sukos they took Aravos 11 Amos tall, so one (the last) Amah was bent over the Mizbe'ach (its corners are 10 Amos tall).
Sukah 45a #2: One who takes a tied Lulav and thick myrtle (it is thickly covered with leaves), the verse attributes as if he built a Mizbe'ach and offered a Korban on it.
Sukah 45b: One who makes an Isur (connection) to the Chag in eating and drinking 1 , the verse attributes as if he built a Mizbe'ach and offered a Korban on it.
Rashi: The Korbanos and Chagigos (Shelamim that every man must bring each Regel) that were clean and checked from blemishes, they tied them to the legs of their beds, until they brought them to the Azarah, on the corners 2 of the Mizbe'ach.
Radak: Bring a lamb tied in ropes to the corners of the Mizbe'ach, i.e. to offer it in front of Hashem. The Korban is called Chag, because most are offered during the festivals. The same applies to "Chagim Yinkofu" (Yeshayah 29:1).
Radak (29): Shmuel said this when he called people to eat from the Korban.
Malbim (28): The king commands the Kohanim to tie the Korban that he brought, and bring it to the corners of the Mizbe'ach to offer it.
Rema (OC 429:2): The custom is to increase slightly eating and drinking on the day after the festival. (Surely this is not considered like building a Mizbe'ach and offering a Korban! Rather, just like during the festival, his eating and drinking was a Mitzvah (in the Sukah, or eating Matzah), he continues to make it a Mitzvah, via eating with intent to have strength to serve Hashem. So I understood from R. Moshe Shapiro. - PF)
Tehilim ha'Mefurash (Diskin): I.e. the blood will go on the corners of the Mizbe'ach. (Usually, 'Keranos' refers to the corners on top. Only Dam Chatas is put on them! Perhaps here it refers to two of the bottom corners, where blood of Shelamim and Olos is thrown. - PF)
