는 (topic particle) and 가 (subject particle) change the meaning slightly by adding additional connotation. Roughly, the phrases can be interpreted this way - but note that the difference is subtle and can vary a lot. 1. 할 수 있다 = It is possible [I/you/they are able] to do something. (simplest - no special nuance). 2. 할 수는 있다 = It is possible (if we/they really try). (implies some unmentioned condition or possibility) 3. 할 수가 있다 = It happens to be possible [It can be done / can happen]. (more focused on the fact of occurrence) 은/는 sets the subject noun as the central theme. This has the additional effect of scoping the meaning, contrasting it with other unmentioned cases. For example, 영철이가 몸은 약하다 sounds like he is good at something even though he is physically weak, like being smart - 는 limits the scope, and this draws attention to other possible things. 이/가 doesn't put as much focus on the subject noun as on what's happening, i.e. the event or action itself. So "할 수가 있었어" says the speaker was able to do it, focusing on that fact only. "할 수는/순 있었어" is like they were able to do it, but that's not the end of the story (perhaps it wasn't done in the right way, for example). Another example. - 원하면 그렇게 할 수는 있어 => If you wanted, you could do it all right. (but I'm not sure if it's the right thing) - 아무리 힘들어도 그럴 수는 없어 = No matter what, I can't do that. (singles it out from the other cases). - 그렇게 하고 싶어, 하지만 할 수가 없어 = I want to do it, but I am not able to. 은/는 often implies an intention or some inherent ability or quality of the subject noun, while 이/가 typically describes (random) happenings. If you include neither (i.e. 할 수 있다), the phrase becomes simpler, without special nuance. It takes exposure to numerous examples to understand them.