The doofus that built a house I bought had a 200 amp panel put in for an all
electric house. We are at the maximum of what will run off this panel.

I want to add a casita, and a shop.

So, I need to run a 400 amp service from the pole to a panel that will feed
the casita and shop. Distance from pole to said box is about 150'.

What size cable would I run from the pole to the 400 amp box?

Steve