  We study the cosmological properties of a codimension two brane world that
sits at the intersection between two four branes, in the framework of six
dimensional Einstein-Gauss-Bonnet gravity. Due to contributions of the
Gauss-Bonnet terms, the junction conditions require the presence of localized
energy density on the codimension two defect. The induced metric on this
surface assumes a FRW form, with a scale factor associated to the position of
the brane in the background; we can embed on the codimension two defect the
preferred form of energy density. We present the cosmological evolution
equations for the three brane, showing that, for the case of pure AdS$_6$
backgrounds, they acquire the same form of the ones for the Randall-Sundrum II
model. When the background is different from pure AdS$_6$, the cosmological
behavior is potentially modified in respect to the typical one of codimension
one brane worlds. We discuss, in a particular model embedded in an AdS$_6$
black hole, the conditions one should satisfy in order to obtain standard
cosmology at late epochs.
