Why does diamond have no molecular formula?
To quote my answer to Is a diamond a single molecule?:

Diamond is a covalent network solid, like a number of other common materials (quartz, graphite, glass, and a whole bunch of stuff).
Because they are not discrete molecules - there is no 'diamond' molecule the same way there are molecules of caffeine, benzoic acid, citric acid, N,N-dimethylaminopyridine, etc.

Another way to think about it, since diamond is a covalent network solid, each diamond is a single giant molecule. Since each diamond is one molecule, there is no universal diamond molecule with the exact same number of carbon atoms every time it occurs.
Fullerenes form distinct molecules with the same number of carbon atoms in each species every time. Thus buckminsterfullerene is always comprised of molecules of $\ce{C_{60}}$.