How to union contiguous objects in blender?

Question

3D

The boolean modifier doesn't work. I want to merge 2 objects so that the internal geometry is deleted.
blend file on Yandex disk ~496kb

Please don't suggest handles, because there are a lot of such cases in the final model...

Answer 1

Here's how the Boolean modifier works:
www.youtube.com/watch?v=lDweCpDAB_o
In your case, I expanded the cube a bit to make a clear intersection between the cube and the corner.
www.pasteall.org/blend/38210