When a mole grows, is it cancerous? or can it be non cancerous?

It can be either: A changing mole raises suspicion that it could be melanoma, yet not all moles which are removed under such a suspicion turn out to be melanoma. The typical yield of melanoma in such biopsies is 1 in 5 turns out to be melanoma. So if a mole grows, you should show it to your doctor or seek opinion from a dermatologist. They may chose to biopsy it there and then or observe closely for some more time.