In general, the question is "what makes someone a human?" and once you answer that you can replace everything else with any parts you wish - robotic, or artificial flesh, or animal parts if you want - that wouldn't make you any less of a human.
As I understand, the current theory says that the mind makes a human. The mind is presumably executed on the brain. Setting aside the far-fetched science fiction of replacing the brain itself, one can say that a cyborg with a human brain would most likely be a human.
There is of course one little catch. If cyborgs have some unique abilities that mere humans don't have then such cyborgs, being humans, will form their own tribes and eventually set themselves apart from the rest of the humanity. So if you start making cyborgs, be aware that they will eventually form a mini-society - unless they are a majority; if they are, then it's unmodified humans who would be hanging together.
The first paragraph and the second are a contradiction in terms.