Rome was a multicultural society with people from all over the empire (including non-white North Africans, berbers and middle easterners) mixed. In fact, it was the barbarian Germanics who were (pure) whites as opposed to the Romans who were a mixture.
As for your assertion of "The white race , if you observe history, has been the conquerors and everyone else, subjected peoples. ", your basic premise is wrong. Ancient contact between east and west were few and far in between because few empires were powerful enough to project power that way. Most of the infighting were going on between empires in their local territory.
Contact between east/west was few before the past 400 years, but still there are examples where the non-whites defeated the whites:
1. Mongol Empire conquered Eastern Europe/Southern Russia (white).
2. Alexander (white) was defeated and forced to retreat by dark-skinned Indians.
3. The Muslims (non whites) conquered the Eastern Romans (Byzantines)'s capital Constantinople/Turkey (white).
4. Muslims (non whites) also conquered Spain (white) and parts of Italy (white).
5. Persians (non whites) conquered parts of Eastern Europe.
6. Muslims (then, mixture of non whites/whites) also conquered Eastern Europe (whites)
7. Some geographers also consider today's Levantine Arabs to be Whites. If that is so, you can assume Muslims also conquered these Levantine people/whites.
The reason why Western Europe wasn't conquered is because it was too far off geographically.
