It depends on the time period and location, but for the most part yes. Most noble children would have had access to high quality education and often learned to speak multiple languages. I just read about this recently but after looking around, I couldn't find the source, so take this with a grain of salt.

In England prior to the Norman Invasion, for example, Monarchs were elected by the Witan and were not necessarily guaranteed the throne based on heredity. Despite that, those eligible would have likely grown up with the kind of education that would have prepared them for such a role. I believe that Godwin's children, for example, were all said to have learned five languages at an early age and would have been groomed to follow in their father's footsteps. People eligible for the throne were typically a ruler in their own right (whether it be as a duke or earl, etc) and would have had the experience necessary to rule. The rare child king would have been surrounded with advisors that, in addition to helping him make decisions, would have taught him how to rule until he came of age.

Sorry for the barebones answer, but I hope someone else can come along and expand on this for you!

Final edit: I've realized my answer may not meet the expectations of the sub and I appreciate the constructive criticism. I'm new here and would like to continue to learn and also contribute. With that being said, please continue to elaborate on the post as it'll help me learn as well. Having just gotten my first job in the field I'm excited to improve myself as a historian on and off reddit.

I can't speak for countries other than England, but generally speaking no, but they were given the education in their own right. Only the heir to the throne was given a "kings education". You can read more about this in Alison Weirs' Children of Henry the VIII or Henry the VIII. She discusses his children's (Prince Edward, Queen Mary I, and Queen Elizabeth I) in the former and his own in the latter.

The heir to the throne of England is given the title Prince of Wales (currently held by Prince Charles). This is where they would begin receiving their formal education on ruling, politics, how to be a statesman, etc. in Henry's case, he was not expected to rule, so he was given a standard education (Latin, music, religion, etc) while his brother Arthur was given a kings education. After his brother died (when he was 9), he began to receive the Kings education. Other royal children are given their own households to rule and manage though, much like dukes or other nobility.

Later in Henry's life, he didn't believe his daughters would ascend to the throne so both Elizabeth and Mary were given a good education, but not a kings education. Luckily for them, they were born in a time where educating women was swiftly becoming be popular thanks to the humanist movement. Women were still believed to be naturally inferior, but that it did benefit them to learn things other than needlepoint, how to raise children, and religion. When Mary, and eventually, Elizabeth came to the throne there was a lot of concern if they were capable of ruling based on their lack of experience and that they were women.