Yes Google does build it's own web servers unlike other data centers who usually buy their servers already made through Dell and other computer companies.
Google not only builds it's own web servers from scratch with parts sourced from different companies the company Google also has it's own server software unlike other web servers who run mostly on Centos or other Linux versions of server software.
Googles software developers write their own server software to operate it's web servers in it's many data centers across the globe.
Google has thousands of web servers in several data centers that host all the videos on Youtube and to take all the searches from Google search that are done every minute.
It also needs a lot of storage and servers for all the websites that are indexed on Google Search for someone to find when they perform a google search.