Can a cancer patient have cbc blood test that are normal or different?

Yes: "cbc" (complete blood count) is a measure at a particular time of how much of the blood is composed of red blood cells, and what the size and hemoglobin content of those cells is, and of white blood cells, including the various different types of white blood cells. A cancer patient who does not have leukemia may have a normal cbc, or depending on treatment, extent of disease, etc may not.