Some forms of cancer yes, probably not all of them. But we can make cancer less common by understanding what situations make them happen more often in us, and avoiding these situations. For example for lung cancer, reducing smoking, reducing air pollution etc..
Cancer is caused by various genetic mutations, and these mutations can happen to us, as we grow up and are exposed to dangerous chemicals or UV light. However, sometimes people have a higher genetic risk for cancer. So certain genes mean you are either born with some mutations and you are more likely to gain mutations through life, increasing your risk of cancer. So while we get better at treating the cancers we know today and treating them I am not sure if we will ever cure all cancers, especially if we see new types of cancer in the future. Medicinal cures and genetic therapies are a race against biology.