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Solutions of Einstein’s equations are found for global defects in a higher-dimensional spacetime with a nonzero cosmological constant Λ. The defect has a (p− 1)-dimensional core (brane) and a “hedgehog” scalar field configuration in the n extra dimensions. For Λ= 0 and n> 2, the solutions are characterized by a flat brane worldsheet and a solid angle deficit in the extra dimensions. For Λ> 0, one class of solutions describes spherical branes in an inflating higher-dimensional universe. Instantons obtained by a Euclidean continuation of such solutions describe quantum nucleation of the entire inflating brane-world, or of a spherical brane in an inflating higher-dimensional universe. For Λ< 0, one class of solutions exhibits an exponential warp factor. It is similar to spacetimes previously discussed by Randall and Sundrum for n= 1 and by Gregory for n= 2.