The Passuk in Ezra (6:3) says that when Koresh gave the Yidden permission to build the second Beis Hamikdash, he told them to make it 60 amos wide and 60 amos tall. The question arises, however, that the Mishnah (Middos 4:6) writes that the Heichal was 100 amos wide, long, and tall. The Rambam (Hilchos Beis Habechirah 4:3) writes that this talking about the Heichal built by the Bnei Hagolah, the Yidden who returned from the exile to Bavel and built the second Beis Hamikdash. (This is as opposed to the First Beis Hamikdash, or Hurdus's renovated second Beis Hamikdash, which were both 120 amos tall, as we will soon discuss.)
The simplest answer to this question would seem to be that Koresh did not know exactly how big it was supposed to be, so he said sixty, but he really did not care, and let them make it one hundred. However, the Medrash says (Esther Rabba 1:5) that Hashem was angry at Koresh for dividing the Beis Hamikdash in half, as during the first Beis Hamikdash it was 120 amos tall, and Koresh said to make it sixty. From this it sounds like Koresh says sixty specifically; and did not let more. One can say that when Daryavesh became king and gave the Yidden permission to continue building the Beis Hamikdash (after the construction was halted by Koresh and Achashverosh because of libels by the antisemites), he let them make it one hundred amos tall, however there is another Medrash (Bamidbar Rabba 14:18) which says that the second Beis Hamikdash was actually built sixty by sixty amos. [see Eitz Yosef on the Medrash there, who raises this contradiction between this and the Mishnah in Middos, but does not answer it.]
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)