As a medical student, and one the first thing that you learn is that each cancer is different. It's true that cells multiply indefinitely, but each type of cancer is due to a specific gene factor (whether is by inhibition of a gene that control cell division, or a gene that induce cell division). So, in order to create a medicine to cure cancer, one must target the malfunctioned gene. The problem with these, gene are no easy to treat since they are found inside of the DNA, which is cell of our body have. So in addition to target the gene, you must target the specific cell affected, which is difficult. Disease such as Duchenne or Osteogenesis are example of disease with malfunction gene, that does not have a cure.
But, this not means that a type of cancer cannot be cure. Each year, research and technology are advancing, making more accessible to create alternative way to cure cancer. So addressing the title of the post, yeah, a cure can be already made but only for specific gene type of cancer (example, a Breast cancer with Her2 gene defect is different from BRAC gene defect, so a cure can only work for the desire gene).
But, this not means that a type of cancer cannot be cure. Each year, research and technology are advancing, making more accessible to create alternative way to cure cancer. So addressing the title of the post, yeah, a cure can be already made but only for specific gene type of cancer (example, a Breast cancer with Her2 gene defect is different from BRAC gene defect, so a cure can only work for the desire gene).