We will consider a four dimensional distributional braneworld embedded in a 6 dimensional spacetime. The geometric setup is akin to finding cosmic string metrics in classical general relativity ie dynamics of codimension 2 defects. The bulk gravitational theory, we will argue, is the generalisation of relativity theory in higher dimensions. In the context of this theory we will present the general solutions describing de-Sitter, flat and anti de Sitter branes as Wick rotated black hole solutions. We will then consider that the braneworld in question carries a distributional perfect fluid. We will then solve the distributional and field equations in the vicinity of the brane. This will provide the cosmological evolution equations for a braneworld of codimension 2 (ie in the context of 2 extra dimensions). The solutions will asymptote the exact vacua presented. We will show that geometric acceleration resulting from the bulk dynamics can provide a small cosmological constant as observed by a four dimensional observer. We will also comment on the validity of the thus obtained modified Friedmann equations.