Centre-half Cuthbert, 25, has made more than 50 appearances for the O's despite missing this season's run-in with a fractured metatarsal.
The club have also offered new deals to defenders Romain Vincelot and Elliot Omozusi and striker David Mooney.
But they are the only four players who will be out of contract in the summer to be offered fresh terms.
Former QPR duo Cook and Rowlands will be released along with utility man Leon McSweeney, striker Charlie MacDonald, goalkeeper Lee Butcher and midfielder Jimmy Smith, who scored in Orient's final-day 1-1 draw against Oldham.
- Sports & Recreation
- Romain Vincelot
- Elliot Omozusi