I don't think that Cain would be doing better if he were white. He might be doing worse. He has significant liabilities as a candidate, and I wouldn't attribute it to racism if the Republicans pass on him.
1) His economic ideas are genuinely kooky and unworkable (and that's supposed to be his strong suit).
2) He knows nothing about foreign policy, and says that he would take advice from people like John Bolton. He won't say what his foreign policy would be other than who he would go to for advice.
3) He said that he wouldn't have a Muslim on his staff because that would mean that America would be ruled by Sharia law. Now he says that he would hire a Muslim, but only if they took a special loyalty oath for Muslims.
That's just for starters.