All those Youtube videos are stored in several different data centers owned by Google in many different states and countries.
Google has 8 data centers located in the USA and one data center in South America, Four Data Centers in Europe and Two data centers in Asia.
Googles Data centers in the USA are located in the States The Dalles, Oregon; Atlanta, Georgia; Reston, Virginia; Lenoir, North Carolina; and Moncks Corner and South Carolina.
So those Youtube videos that are uploaded to Youtube could be stored in any of those data centers on any one of those web servers.