Is there any difference between "3-dimension space" and "3-dimensional space"? We should use "3-dimension space" or "3-dimensional space" to mean a space with three dimension? Why?
The answer is 3-dimensional space. There's no grammatical reason I can give you. It's just due to common usage.
This is a really good question.
There are others:
3-bedroom house or 3-bedroomed house
3-leg stool or 3-legged stool
Sometimes the adjective wins and sometimes the noun (playing the role of of an adjective) wins. It's a usage question not a grammar question.
Sorry for such a disappointing answer.
More on compound adjectives