I am 1/128th Cherokee. Outside of having hardly any body hair, as well as the ability to keep a great reddish-colored tan, I'm white...but your question is more complicated than just observing blue eyes and European features.

Most people can do the math after looking at their genealogy, though it can get complicated if several Cherokee bloodlines are input and diluted from multiple family lines leading to yourself...i.e., somebody was 25% Cherokee married someone that was 50% Cherokee, and their kid married someone with 10% in the bloodline, and their kid married someone with 0%, but their kid married someone with 5%, etc.

Mine is easy to calculate, and for simplicity purposes I'll assume his is the same. At some point, a 100% Cherokee entered his family, creating a child that was 1/2 Cherokee. Every generation thereafter lacking an additional input of Cherokee bloodline cuts the bloodline in half, i.e. everyone else marries white...so 1/4, 1/8, 1/16, 1/32, 1/64, then 128th...meaning his greatX5 grandparent must be 100% Cherokee and each of his other grandparents since, male and female, had 0% Cherokee lineage.

To answer your question, is he white...well that depends on perspective. To get federal protection status he must have formal membership in a federally recognized tribe, and even then it depends on which federal programs you apply for benefits/protections/etc. The requirements to get into a tribe vary. Some tribes require as much as 1/4 blood quantum to join, and an even more concentrated bloodline to hold leadership positions. Others, like the Cherokee Nation, only require proof of lineage from a tribal member that can be found on their historical rolls, regardless of the dilution of the bloodline. Some recognized tribes feel a blood quantum requirement is racist and self-demoting...not to mention self-defeating since perpetual dilution is inevitable over time. For the culture to survive, it's important for those with the lineage to remember and embrace it.

I know very little about the Cherokee culture, so I'm no champion of the Cherokee cause...but if your buddy wants to embrace it, and he has the lineage to add legitimacy, then don't break his balls about it...because he's only a few letters and forms away from having federally recognized membership in a tribe, and then what'll you say?