I think your colleague is upset about your comment to everyone in the room, not failing to clean the machine. You could have left without a coffee or a comment. By making an announcement, perhaps in a tone that said "I am making a joke here" you implicitly criticized the sign. Or perhaps your comment might have sounded like "oh hahaha I love drinking your coffee but I never clean the machine, who would do that, I am too important to clean machines, I'm going to go get coffee somewhere else because I like other people to clean up after me." That isn't what you meant, but it may be what they heard.
Since your colleague won't stop bringing it up, you need to make things right in order to go back to a normal office atmosphere. Next time you see the colleague, say something like "I never expected to upset you by poking fun at myself about the coffee machine." This may lead to an immediate argument that you were in fact poking fun at the sign or the colleague himself, or that you were saying laziness is good, or any other number of things that this colleague has been brewing in his head for a while. If that happens, deliver a sincere apology:
Oh, wow. I am sorry. I've really upset you with that comment. It was thoughtless. I will be more careful making jokes in the future.
Do not say you are sorry IF the person was upset: you know darn well they are upset. Do not say you didn't intend to upset them; while useful information, it is not part of an apology. Acknowledge what you did clearly and name it. Then talk about how you will make it right. Don't make it right by cleaning the coffee machine: this is about how you spoke, not what you did or didn't clean.
If your "I never expected" line above just leads to a grunt, or a "well, you did" then your apology can't be quite as direct. You could say something like
I'm sorry. Since you keep mentioning it, I must have upset you with that thoughtless comment. I will be more careful making jokes in the future.
Don't press the colleague to agree they were upset, nor to accept your apology.
In either case, if the colleague brings it up again after you've genuinely and properly apologized, you can now say something like
Is this going to be a thing for the rest of my life?
or, if no-one else is around
Are you ever going to drop that? I have apologized. Is there something further you are expecting from me over my thoughtless joke 10 days ago?
Don't do that in front of people, it's a little confrontational, and embarrassment in front of others is what started all this.
I went to the neighbour office where I always get my coffee
. what?