Stealing sweets and killing 5 people for inheritance and blaming one of the victims is just a tad different. Bamber won't admit to the crime because he would have to admit to being a child killer. He has no choice about doing the time, his choice is in taking responsibility or not. The evidence is the cold and callous nature of his crime and his continued denial.
I don't think his killing spree is evidence of him being a psychopath. He did kill in cold blood because he wanted to and may have enjoyed doing it, but that can be put down to a 'single incident' where as, do we believe he would become a serial killer in the public domain had he been set free? No one knows and predicting is not a science.
He is enjoying his manipulation and adulation he has acquired- all swings and roundabouts. He knows he is guilty- he just doesn't want to be punished for it. That was the reason I mentioned the child with sweets.