The data behind whether "black men [are] really bigger" is shakey.
There are websites such as the one below that have listed average erect length by country, which one
could use to generalise by race, but one shouldn't, and I'll explain why later.
Average penis size by country: worldwide comparison
For example, in a country like Cameroon (which has a demographic profile of almost entirely Sub-Saharan African), you could theoretically use it as an example for black men and compare it to Korea (where the demographic profile is almost entirely ethic Korean) and so on and so forth, and say that by comparison, "black men [are] really bigger".
In fact, in this list, of the top 20 countries listed, 10 are have demographics where the majority are black.
However, to use this to draw a conclusion on the question at hand would be problematic. We don't know the source of this data, the number of participants, whether or not they self-reported their size, if they were classed by country of brith or by current nationality, or any other factor that would allow us to say with statistical certainty that it represents anything, not actual national averages and definitely not racial averages.
And in fact, there are numerous other studies that show that there is very little variability between average length and race.
Herbenick et al. for example, measured a variety of people in the US from different ethic backgrounds and race and found statistical differences in length on average of only 1 cm.
There was another study in Brazil where participants had to self identify as black or white and they were subsequently measured, instead of asked to self report length, and the researches found a difference in length, but it only amounted to just over 1cm.
Anthropometric study of penile length in self-declared Brazilians regarding the color of the skin as white or black: The study of a Myth
It's difficult to say whether or not black men have larger penises on average, so we rely on anecdotal and self-observed 'evidence'. Also, there is the problem of bias, where we are subconsciously fed that black men are larger, and this is true in porn specifically. Is this a representation of reality? Probably not, but maybe.
In the end it's hard to say whether its true definitively as a very large scale study would need to be done, something I don't see ever happening, as the funding would need to be quite large, and let's face it, no one really cares enough to throw that much money at this question.
