On the edges of my cubes, lines with RGBA 0, 0, 0, 0 appear as texture lookups on that position fail. I have colored the texture lookups that failed magenta in my fragment shader.
Should I render to a texture first, bind it to a quad and perform the MSAA afterwards instead of per cube?
Maybe it samples pixels that are not filled yet.
Using GL_CLAMP_TO_EDGE
instead of GL_CLAMP_TO_BORDER
solved the issue.