Not whole weekends- late Saturday night, up to 12:30 on Sunday I think is the case every weekend. Looking at the East Coast timetable for 4th March (which shows ONLY EC services- no Scotrail etc), there's four northbound services that appear to go via Cambridge, plus one starting at Peterborough, one at Retford, four at Doncaster, one a York and one at Edinburgh. Southbound, there's a service that terminates at Peterborough, one at Doncaster and four through via Cambridge.
I'd assume that all through services will be HST.
Hull trains don't operate during the closure time anyway, and GC are fully cancelling a north and southbound service on both routes those days (despite 180s certainly being cleared to Cambridge, as GC and HT have operated to and from there in the past)