"Draw on" and "base on" mean different things. "The scientists based their research on their experimental data.", but: "in his book on History, he draws on many other history books."

To me, 'draw on' suggests a less concrete relationship than 'based on'. If A is based on B, that means that B plays a large part of A. If A draws on B, then B plays a smaller part of A. In other words, A is based on many different things, and B is just one of them.

It depends, of course, but "base on" or "based upon" or "based on" is typically going to be what is used. "Draw" is often used in this context: "You can draw (come to) the conclusion..." Meaning the person came to a conclusion (an answer). A typical sentence might read something like "His conclusion was based on the information." If you want to write several examples, I would be glad to help.