In times past, students of the Bible have suggested that modern racial divisions can be traced to the three sons of Noah (Shem, Ham and Japheth). The most common view assigned Shem as the father of Semitic/Asian peoples, Ham was regarded as the ancestor of Black Africans and Japheth was said to be the progenitor of Caucasian/European peoples.
However, it is interesting to note that race is not mentioned in Scripture. Instead, the Bible speaks in terms of families, tribes and nations. Hence, the assignment of racial categories to the descendants of Noah's sons is based on human interpretation and extra-biblical information. In short, the racial divisions of humankind cannot be demonstrated exclusively from the Bible!
It should also be noted that modern genetic research has turned our traditional understandings about race upside down. Skin, eye and hair color are now understood to be very superficial features that don't really tell us much about what's on the inside of a person. Also, any view that talks about a White, Black and Yellow race has been demonstrated to be very simplistic at best and probably worthless in the final analysis when discussing human populations.
The study of human DNA has demonstrated that we all ultimately originated in Africa. More particularly, the study of mitochondrial DNA has demonstrated that humanity is descended from a common female ancestor that lived about 200,000 years ago known in scientific circles as "Mitochondrial Eve." Similarly, genetic scientists have determined that all paternal haplogroups derive from a "Y-chromosome Adam" that lived about 150,000 years ago. It should also be noted that there is enough wiggle room within the scientific evidence to suggest that these two ancestors of the human race could have lived at about the same time. Nevertheless, the bottom line is that we are all related to each other either way (through the genetic or biblical model).
It is also interesting to note that many folks have submitted their DNA to labs for testing in connection with their pursuit of the story of their ancestry. Indeed, Genetic Genealogy is one of the fastest growing branches of ancestral research in the world today. This testing has completely upended some folks' conceptions of who they are and what race they belong to. Many "Black" Americans have discovered that they have significant percentages of European ancestry in their backgrounds. Likewise, many "White" Americans have been surprised to find that they are descended from an African haplogroup. My own genealogical research and genetic testing has revealed European, African and Native American heritage. Taken together, this demolishes any notions of ethnic or racial purity that have been advanced by some folks.
What is the conclusion of the matter? God created a wide range of genetic possibilities, but all of the evidence (both biblical and scientific) indicates that "He" did not create races of people. On the contrary, the evidence demonstrates that people and geography have led to the formation of these superficial differences among the human race. Hence, there is no Divine mandate for racial prejudice, and there really is no such thing as miscegenation.