Nope you're one or the other or both, culture is not shaped by race and never was it was shaped by simply surviving and crossing paths with other people, for example the UK is shaped by it's history of different civilizations and tribes from across Europe invading, each brought new changes and approaches to living in the same environment.

Jewish people came from Africa into Europe and the Middle East trying to escape various empires like the Egyptians and the Romans, Judaism itself ended up spawning Christianity and Islam which impacted many cultures in future, this is an example of culture not being shaped by race. Another example is Hinduism also spawned East Asian martial arts as a Hindu travelling monk arrived in East Asia to find people lazy and made them train in combat to rid them of their laziness, this ended creating things like Kung Fu which East Asia is famed for in their cultures as well as orders like the Shaolin Monks.

These weren't cultural things that happened due to race no these are examples of cultures being molded by surviving and people crossing paths.

Specifically the Ashkenazi Jews ... (Would definitely be interested in having more studies involving them.) 

Hispanics are also in the middle of the pack if we consider them genetically diverse enough from existing races ... 

Africans also might be in the middle when we have Australian Aboriginals ... 

Personally I think too much emphasis is put on tests like these. 

If that is the case, then Americans should have higher IQs than their (presumably) dumber European counterparts, as America has clearly overtaken Europe as the global leader in cultural, financial, military, etc. relevance. 

Also Western Europeans must be much smarter than Eastern Europeans in that case. 

According to the APA report the heritability of intelligence is still 0.75 (that's still high) when you're an adult so I'm not sure how one of my source using mostly western countries for sampling changed anything about my conclusion ...

Because you're trying to say that certain races are somehow superior to others, yet showed me a report that compares people of the same race.

"We conclude with our own less elegant commentary regarding how these findings should be understood and the role of the environment in the shaping of human psychological traits. It is important to specify the populations to which any results can be generalized and not misinterpret what they mean. The samples were drawn almost exclusively from Western industrial democracies. These settings have characteristic environments. Only a few of the participants were raised in real poverty or by illiterate parents, and all study participants had access to the contemporary educational programs typical of those societies. This is the domain to which we can generalize. The results do not mean that environments are irrelevant or unimportant. The proximate causes of variance in IQ are the ‘cognitively stimulating experiences’ that the individual is provided with and seeks for him/herself. Early in life, those experiences are primarily imposed (or not imposed) on the individual and that shows up as shared environmental influence. As the individual becomes more of an independent agent, the effective experiences are to a large extent self-selected. As Martin et al. (1986) put it: ‘humans are exploring organisms whose innate abilities and predispositions help them select what is relevant and adaptive from the range of opportunities and stimuli presented in the environment. The effects of mobility and learning, therefore, augment rather than eradicate the effects of the genotype on behavior’ (p. 4368). This idea has been elaborated in some detail by Scarr (1996) who has argued that people make their own environments¹ and Bouchard (1996, 1997; Johnson, 2010a), who has elaborated the Experience Producing Drive Theory of Keith Hayes (1962)."

How does this prove anything? IQ does have a heriditary factor so? It also has to do with the Socioeconomic state, teaching and many other factors.

Even if it does have a heriditary factor, how many of us know a family where one sibling is very smart (at least in terms of school grades) and yet they have a sibling that is far from it? 

Happens all the time, and that's from about as geneticially "pure" of a sample as you can get (the same exact parents). Applying such broad generic generalizations to huge groups of people makes even less sense. 

But Americans don't have a higher IQ than their common european counterparts as shown with recent study ... 

Have you seen the average IQ scores of each race ? You'll know what I mean when you look at the numbers ...

They kept killing their girls because of the one child rule which now I believe has been amended.  Women are in short supply in China and I believe they are even shipping them in from neighboring countries.  So they perhaps will be less Chinese and just more mixed with their Asian neighbors.