From a young age, children can tell "differences" in appearance. Not "race" per say... but differences in appearances.
At home there may not be a emphasis on it and both cultures/races are evident & accepted, because of the parental influences on it or not.
But, outside, in public... there is a strong need for people to identify with either or. ie: either black OR white. Outsiders, the public view, do not "see" mixed race children as both.... ie: Barack Obama. HE is actually white (from his Mom) AND Black (his Dad). BUT the public view of him is that he is "black." They do not emphasize his "white" side nor use the term "white" to describe him.
But it is also the overall culture of the community you live in. In my State, there are MANY bi-racial or mixed race/mixed culture children. And it is accepted and it is common here. There are many children of varying skin colors, which reflects their multi-cultural heritage. And the various cultures all intermingle and the cultural practices are practiced.
My family are mixed Caucasian/Asian, and other things, and in both sides of the family.. And it is common here. Thus, the children do not grow up with having to compare themselves or to "be" one or the other, and their identities are intact and confident and they don't feel any "different" than the others. And they don't get hung-up on skin color or eye color. And they KNOW both cultures. It is not confusing for them nor a big deal. Because in my State, there are so many different cultural groups anyway.
Mainly, it is how they are raised at home... to feel comfortable & confident with their appearance/culture/heritage, and to understand that people come in all sorts of "colors" and cultures. So that they too accept themselves. BUT... per each age, they may have developmental phases where they naturally "compare" themselves to others and have preferences. Your child, probably is perhaps identifying with his Dad... and his appearance. Maybe he just wants to look like Daddy or be like Daddy. Not specifically meaning "white"... but in terms of appearance. Then as he gets older, he will have other phases of development.
If you don't want him to think being "brown" is a "bad" thing... it all comes from teaching them at home. That the world is made up of all kinds of people, but we are all the same inside.
At this young age... I don't think your son is thinking in terms of "race" per say. But a child, notices "appearance." And it is also normal that at certain ages... they experience individuality and preferences in many ways. It is how they develop.
But, if a child is exposed to terminology such as "white", or "black" and "categories"... then they will learn that. Just as they learn colors/numbers/shapes in school. It is how a young child "organizes" their world. Kids even compare how other kids dress or what they wear. So... in a general way... this is what your child is doing, probably. He probably just thinks blue eyes looks nice. Nothing more, nothing less.
But, a child will learn "attitudes toward" certain concepts. So... in this regard... teaching a child how to think about "differences" in the world, is important. And they do absorb what their parents feel about it, for better or for worse. So, it is important to teach a child a non-biased view of it.
And to help them feel confident about themselves... not just in terms of their skin "color" or appearance. If appearance is emphasized... then a child will also focus on "appearance'... for better or for worse. So teaching them about WHO they "are"... and accepting their interests/talents and overall personality is also key... not just focusing on either/or "race" or skin color.
Focus on the OVERALL person/identity of the child. Not just "race." So that the child develops a broad sense of self, And confidence about themselves... that is NOT derived from their "skin color" or appearance.
All the best, just some ideas,
Susan