A pasting diagram is the analogue of composition of arrows in higher categories. The nlab page gives an example of a two dimensional diagram and how to compute it as a composite of two morphisms. I am looking for an analogue of this result in higher dimensions. i.e. two n-cubes sharing an n-1 dimensional face.

It's hard to draw the picture, but the guess for the answer, for example in 3 dimensions, is something like (1-morphism $\circ$ 3-morphism) +(2-morphism $\circ$ 2-morphism) +(3-morphism $\circ$ 1-morphism) where the first morphism is given by an edge of the first cube etc.

I didn't find the references on the nlab page really useful.