What phinds says is correct. If the Universe had an "outside" then it would not be the Universe. The Universe can be defined as: "the totality of everything that exists" therefore if something exists, by definition it is part of the Universe.
For their to be an "outside" would also require a "center" and an "edge" which would invalidate the cosmological principle of isotropy.
We can, however, measure curvature from within the metric to determine if space is euclidean or not - unfornutaley the degree of error is rather small and it is entirely possible that out little patch of the Universe we can see (The Observable Universe) is too small a piece of the whole (Whether finite or not) to determine curvature with any acceptable margin of error.
Global curvature is the key to the "shape" of the Universe in my opinion.
Hope this helps.