The Parah Adumah was burned on top of Har Hamishchah, which is Har Hazeisim, the Mount of Olives. (The ashes of the Parah Adumah-red heifer were used to purify people from Tumas Meis.) This place was located directly to the east of the Beis Hamikdash, as learned from the Passuk (Bamidbar 19:4) "Elazar the kohen shall take some of its blood with his finger and sprinkle it directly towards (אל נוכח) the face of the Tent of Meeting seven times". From the words directly towards (אל נוכח) we learn that number one, he sprinkled the blood towards the entrance of the Kodesh Hakodoshim, and number two, that the location he was in must be directly opposite the Kodesh Hakodoshim. (The face of a building is the door, although from the fact that the passuk does not just simply say door, we learn that over here it also means the most important part of the Heichal, the Kodesh Hakodoshim. In order to see the entrance to the Kodesh Hakodoshim, however, you had to look through the door of the Kodesh. [Tosafos Chadashim, Parah 3:9])
Leading from Sha'ar Shushan, in the eastern wall of the Har Habayis, there was a long Kevesh-כבש ("bridge") that led to the place where they burned the Parah Adumah, on Har Hazeisim. (The ashes of the Parah Adumah-red heifer were used to purify people from Tumas Meis.) This place was located directly to the east of the Beis Hamikdash, as learned from the Passuk (Bamidbar 19:4) "Elazar the kohen shall take some of its blood with his finger and sprinkle it directly towards the Tent of Meeting seven times.
I have added a new video of the Lishkos on the northern side of the first Beis Hamikdash..
My name is Mendel Lewis.
Hashem said to Yechezkel, "Its reading in the Torah is as great as its building. Go and say it to them, and they will occupy themselves to read the form of it in the Torah. And in reward for its reading, that they occupy themselves to read about it, I count it for them as if they were occupied with the building of it. (Tanchuma tzav 14)