You have to declare the grades as noted. Honestly my perspective is that it only really makes a difference to resit English language and/or maths to reach minimum requirements and anything beyond that isn't really a good use of time. As basically any courses/unis (bear in mind that Oxford and Cambridge look at GCSEs very differently, and this also varies across the courses offered at each to some extent) that do put a larger amount of weight on GCSEs will normally be less keen to see a lot of resits, and the ones that don't care about resits generally tend to put less emphasis on GCSEs anyway.
In general Oxford tends to care about GCSEs more than Cambridge, although at Oxford this can vary as courses like physics, maths, CS, and similar tend to not really be overly fussed about less relevant GCSE subjects. At Cambridge they're just considered holistically with the rest of your application, although several of the official rep ATs we've had on TSR now and in the past have indicated they had not yet to that point rejected a student solely on the basis of GCSEs in any event.
Grade 6 in English language and maths will fulfill the minimum GCSE requirements for most other unis (note Cambridge doesn't have any formal GCSE requirements - not sure if Oxford do) so I don't see it as a good use of time really.