It is well known that every closed, oriented, simply-connected four-manifold $M$ is homotopy equivalent to a CW-complex consisting on a 0-cell, a wedge of two spheres and a 4-cell.

I was wondering if similar results hold for higher dimensional manifolds, in particular for closed, oriented, simply-connected and spin manifolds in dimension eight. In particular, I would like to know if a closed, oriented, simply-connected and spin 8-manifold admits a "simple" type of cell decomposition.

Thanks.