I’m trying to find a way to render adjacent cubes which have rounded corners in the style of Not simply a "rounded" cube, but only on the edges which do not have a touching neighbour cube.

I.e. the edges circled in red on the crude diagram below. I don’t want to create a model in Blender and use that as the shape can/will change depending on the blocks that I put together.

Here you are some code sample to appreciate. Of course, it needs some work to polish the rounded corners, but I will let this up to you. Cube positions are set in line 66, so you can try with other configurations:

This was almost precisely what I was looking for, thank you so much for taking time out of your day to share this approach! It’s close enough to be able to solve my needs so I’ve marked it as the solution.