What year do cancer experts predict we will successfully treat most cancer cases?

Hard to say. Technology, particularly genetic research, is improving rapidly. This can accelerate the rate at which a cure is arrived at. An exact time it will take is still hard to say since new cancers might be found or occur due to new products, etc., and old cancers may mutate, or recur.
It's pretty good now. No disrespect is intended. When I was a kid, two out of six cancers that were discovered were cured. When I was a medical student, it was three out of six. Now it is four out of six. All multicellular organisms will die of cancer if they do not die of something else first -- it's the nature of life as we know it -- but we're doing pretty well, largely due to earlier detection.