Query posts ordered by category (hierarchical)

Hi,
is there a way to query the posts ordering by their category?

For example, I have this category tree:

1) Cat1
2) Cat2
2.1) SubCat1
2.2) SubCat2
2.2.1) SubSubCat1

And I want an output like this:

1) Cat1
–Postcat1
–Postcat2

2) Cat2
–Postcat2

2.1) SubCat1
–PostSubCat1-1
–PostSubCat1-2
–PostSubCat1-3

2.2) SubCat2
–PostSubCat2-1
–PostSubCat2-2

2.2.1) SubSubCat1
–PostSubSubCat2.2.1-1
–PostSubSubCat2.2.1-2

Please, help me, I’m getting crazy for this ??