Why wasn't China partitioned before anyways? The European took over an entire continent but no China? why?

I assume by the "8 powers" you mean the Eight Nation Alliance. The simple answer to this question is that they did not have the intention nor the manpower required to do so.

You see, the primary purpose of the Eight Nation Alliance's intervention in China was to crush anti-foreigner rebels, and maintain continued access to the lucrative Chinese market, which would otherwise have been cut off should the rebels have succeeded.

The picture often painted of the Boxer Rebellion tends to be one of the western armies fighting the Chinese. In truth, the westerners paid the Chinese armies led by men like Yuan Shikai to fight the Boxers on their behalf. Now, the actual western forces sent into China were certainly capable of winning battles, but conquering and holding a country is another matter altogether, and letting their Chinese warlord mercenaries (of dubious loyalty) hold conquered territory for them was a questionable decision.

Instances where the colonial powers have taken over entire continents (the Americas) and subcontinents (like India) are also reliant on the region being 'less civilized' - that is to say, decentralized and/or being technologically/structurally lacking. This was not the case in China, which had a centralized (if albeit weak) government, a coherent unified Chinese identity, and while technologically lacking nobody could call China 'uncivilized' by any measure.

If you look at the numbers of the regular armies of the Eight Nation Alliance at the time, their combined might was just over 3 million. Obviously not all of that fighting force can be sent halfway around the world, leaving their home territory and other holdings unguarded. Then take into account the Chinese population was 150 to 400 million at the time.

All these factors taken into account means that here was no way the Eight Nation Alliance could have possibly conquered and held all of China between themselves. And the colonial powers were not wont to partition lands peacefully between themselves anyway, there was always fierce bickering in such an event. Japan, Germany and Russia certainly wanted to carve up China like you proposed, and that desire was blocked by countries like the USA.

That being the case, the Eight Nation Alliance, after their victory over the rebels, were content with peace terms that forced the Chinese market to remain open with generous trading benefits for them. In this way, they hoped to reap the profits of colonialism without actually having to administer a colony the size of China.

References:

• Silbey, D.J., 2012. The Boxer Rebellion and the Great Game in China: A History. Hill and Wang.

• Preston, D., 2000. The boxer rebellion: the dramatic story of China's war on foreigners that shook the world in the summer of 1900. Bloomsbury Publishing USA.

• MacKinnon, S.R., 1980. Power and politics in late imperial China: Yuan Shi-kai in Beijing and Tianjin, 1901-1908 (No. 24). Univ of California Press.