[api]

AFAIK the massive influx of cash into universities for the last 30 years or so has gone into administration, which is basically a jobs program, not academics.

[TSiege]

I believe that's tuition. Grants fund scientists research directly. It funds labs, hires grad students, etc

[dotnet00]

A decent chunk of the grant money goes to the university, and a chunk of the money used to pay the students also loops back to the university in the form of non-tuition fees, rent etc.