One of the biggest differences between the United States and Rome in the late Republic is how politics played a role in society. When did patrician and plebeian males start learning about politics, and at what age?
We know of (especially Greek) slaves who were able to read and write and were often educated very well in terms of rhetoric, math and other subjects. They often served as private teachers for rich families. Sometimes even girls/women were taught - for example the younger Pliny's wife (a little too late for the late Republic) could read and write.
A more expensive way of education (because of that exclusively used by highest nobiles) was to send the young politician in spe to prestigious teachers. The schools for philosophy and rhetoric in Athens, Rhodos and Alexandria were famously known in Rome. As far as i know Cicero himself went to Rhodos after his first education in Rome to improve his rhetorical skills (speech and stylstics) - his Œuvre proves his success in doing so.
Political education was for sure brought to the children in their fathers' houses too, but the cursus honorum coined the politician much more. Consecutive offices in different parts of administration had to be absolved to reach highest political honours and powers, which applied necessary skills to the politicans "learning by doing".
At the same time it helps to understand at which age the education took place: The first administrative office, the questor's post was available at the age of 30 (25 since Augustus' principate) but before beeing officially allowed to access this post one had to serve in the army for 10 years as military tribune. Because of this, the private education has to be more or less "finished" by the age of 20 (under Augustus even earlier) in order to perform a straight curus honorum.
There were always exceptions to this systems: Pompeius for example did not follow the curus honorum by any means and still is known as a shining light of the late Republic. It is also known that the military component was often skipped or massively shortened.
So i would argue that private education in the villa patris or with local teachers (especially in cities and villages other than Rome) must have begun in young child's age, maybe at the age of 6-8 years.