It depends how you define a Data Center.
Some define it as the physical building but it really is not.

You can still call a Cage or a Private Suite a Data Center... because the equipment and the technology used to run it is whats establishing it a Data Center.

A Building like One Wilshire isn't the Data Center because they have other operations like Office Buildings that run in their as well.

Someone like ThePlanet may be a large Provider but 2 or 3 of their Data Centers are infact cages or Private Suites at a Telecom Hotel.