you are correct... a subreport cannot have a subreport.
well you can't really run a report more than once... you would need to change the parameters and run it again...
you could schedule it 16 times...though to be honest I know absolutely nothing about that, I've just read where people have had issues.
you could structure the report to run once but return what appears to be 16 reports via grouping and resetting the page number
those are basically the 2 methodologies that I can see to accomplish what you want.
HTH