I'm not completely certain of the timeline of the series, book and show (nor am I willing to look one up in case of spoilers), so this may seem like a stupid question...Cersei was "consoling" Catelyn about Bran when she mentioned that her first son died in infancy. She described him as a "black haired beauty" and said he looked like his father, Robert. Since this child was born before Joffrey (14 I believe in the series) and it would make sense for there to be a fairly long period before Cersei would be willing to have children with "Robert" (as we all know, he is not the father of Cersei's 3 blonde children), an interesting question arises, at least for me...Is it possible that Jon is actually Robert's child? The history behind his birth, if I remember correctly, seems somewhat muddled. And, though I don't know when Robert and Cersei were married (again, unwilling to look it up for fear of any possible spoilers), it would seem to at least be a possibility, for Ned would have been with Robert at war at about that time period, and, for whatever reason, could have possibly ended up with the "dead" child, and have lied to Jon all these years about his true heritage. At the very least, the actors who play Jon and Robert look like they could be related, at least more-so than Ned and Jon...Whether that is a coincidence or not is beyond me.
Anyway, sorry if this seems like a stupid question, but I am curious...I don't need any more information on it other than a simple yes or no, or even "it's possible...".