I was watching a show and it seem like there is a slight difference between them. So the conversation was
A:3번 파트 할 수 있어? B:저요? 할 순 있어요.
I get it that 순 is a short form of 수는 but why would you word it like that? in contrast to 할 수 있다 which translates to I can do it how would you translate that
It also means B can do it, but implies that B is not willing to do that, although B will do it if it is necessary. So it is not a strict refusal, but just a sign of mild dislike. If I was there, I would think that either B does not consider that as a good idea, or just B doesn't feel like doing it. A natural response by A is "그럼 할래? 아니면 다른 좋은 생각 있어?" which means "Then will you do it? Do you have any other suggestion?".
In the sentence "할 수는 있어요", 는 is a marker for implicit contrast. The implication depends on the context.
As the primary meaning of 있다 is to be present and that of 수 is an ability or method/way to handle something, "할 수 있어요" means "There is an ability/way to handle (it)" in the literal sense. It usually translates into English as "(I) can do it," but, as you well know, "할 수는 있어요" has the same translation. This is a reason that you cannot easily catch the difference between them.
To understand the difference between "할 수 있어요" and "할 수는 있어요," you should focus on the word(s) preceding 는 because the presence of either 할 수 or 수 is being contrasted with the absence or presence of another noun (phrase). Although the noun (phrase) is hidden (unless the speaker directly mentions it), we can still guess it. What would it be?
Since everyone has their own perspectives, there can be various implications for the same sentence. "할 수는 있어요" may imply one of the following:
할 시간은 없어요. ("I do not have time to do it.")
확신은 없어요. ("I am not sure (if I can do it).")
자신은 없어요. ("I am not (self-)confident.")
문제가 있어요. ("There is a problem (about it)." / "There are problems.")
다른 수가 있어요. ("There is another way (to handle it)." / "There are other ways.")
불만이 있어요. ("There is discontent.")
하고 싶은 마음은 없어요. ("I don't feel like doing (it).")
제가 해야 하는 이유가 있어요? ("Is there any reason I need to do (it)?")
Whichever or whatever it implies, I believe that you have already noticed the difference between "할 수 있어요" and "할 수는 있어요." Of course, there are other ways (for instance, "다른 사람이 더 잘해요" ("Others are better at doing it") and 저도 바빠요 ("I am busy, too")) to discuss such implications without using 있어요 or 없어요, but I thought using them would be better for your understanding since I had mentioned the word contrast. In short, "는" can add a meaning to "할 수 있어요" without revealing directly what the speaker means.
