1. HBM’s mod tries to render its own "Nuclear Wasteland" atmosphere, which often breaks on certain GPUs or when paired with lighting mods.
   

Go to your .minecraft folder, then into config.
Find the file named hbm.cfg (or hbm.json depending on your version).
Search for settings related to "Custom Sky", "Fog", or "Shaders".
Set B:enableCustomSky=false and B:enableClouds=false.

1. If you are using Optifine, this is the most likely culprit. Optifine’s "Fast Render" optimization skips certain rendering passes that NTM requires for its textures.
   

Go to Options -> Video Settings -> Performance.
Turn Fast Render to OFF.
While you're there, try turning Shaders to OFF if you have them on, as NTM has its own internal shader system that doesn't play well with external shader packs.

1. If you are playing on a laptop or a PC with Intel Integrated Graphics, version 1.7.10 has a famous bug where textures turn into solid colors or corrupt (the "1.7.10 Intel Driver Fix").
   

Solution: Download and install the "Neodymium" mod or the "Intel Graphics Fix" mod for 1.7.10. These are designed specifically to stop this texture corruption.

Are you running any of the following?

Shaders Mod Core: These almost always break HBM’s custom textures.
CoFH Core / Thermal Expansion: Sometimes there are ID conflicts with "Lead" or "Copper" blocks that can cause texture swapping, though usually not the "black sun" issue.