I can do it = PERMISSION – human authority / rules and regulations allow me to do it. I can do it = POSSIBILITY – external circumstances allow me to do it. I can do it= ABILITY - inherent properties allow me to do it. (There are times when these meanings overlap.) So, Can you help me with my homework? PERMISSION: will mum, teacher, the examiner allow it? POSSIBILITY: if you don't have anything else to do. ABILITY: are you clever enough/have you got knowledge of the subject ................ The thing to ask is whether be able to also have the same meanings: Are you able to help me with my homework? PERMISSION: will mum, teacher, the examiner allow it? (Seems to be OK) POSSIBILITY: if you don't have anything else to do. (Seems to be OK) ABILITY: are you clever enough/have you got knowledge of the subject? (Seems to be OK) .......... So, up to now, it seems as if both convey the same meanings. ........ states (fact), be able to is normally preferred. "Most people worked harder than me during the University, of course, and when it came to the exams, they were able to draw not just upon two weeks of knowledge. They were able to draw upon three years of knowledge". ..