"I never did it."
Translation:저는 한 적이 없습니다.
한 적이 없다 = Never did = Did not ever (at any time)
안 했다 = did not
한 적이 없다 = 절대로 안 했다, where 절대로 = ever
"한 적이 없다" focuses on the negativity of the time factor of the action (defined by the verb) while, "안 했다" focuses on the negativity of the action itself.
Note: 안 하다 also carries a connotation of unwillingness to carry out the action.
안 했다 = I did not (because I did not want to)
In a sense, but in that way it would actually mean something different.
저는 한적이 없습니다 = I never did it/I've never done it (here you're saying you've never experienced doing something before)
저는 안 했습니다 = I didn't do it (here, you're denying having done something, rather than saying you've never done it before)