  We find numerical solutions of Einstein equations and scalar field equation
for a global defect in higher dimensional spacetimes ($\geq 6$). We examine in
detail the relation among the expansion rate $H$ and the symmetry-breaking
scale $\eta$ and the number of extra dimensions $n$ for these solutions. We
find that even if the extra dimensions do not have a cigar geometry, the
expansion rate $H$ grows as $\eta$ increases, which is opposite to what is
needed for the recently proposed mechanism for solving the cosmological
constant problem. We also find that the expansion rate $H$ decreases as $n$
increases.
