I realise that Shakespeare's plays aren't historical documents and contain many historical errors and that he took many liberties with the stories. They are though based on an essence of truth.
It is widely believed that he attended King's New Grammar School but did not go on to university. Would the education system at the time have taught basic Plantagenet and/or Roman history? If not where would he have learnt enough to write the plays that he did?
/u/legallysparkly has answered this as part of How accurate were Shakespeare's histories?
/u/texpeare has previously answered Which is Shakespeare's most historically accurate play?
/u/CatieO has previously answered What was the general level of historical education of Shakespeare's audiences? (paraphrased title)