I think I found a driver bug and would like to report this one.
Uploading to a GL_TEXTURE_CUBE_MAP with glTextureSubImage3D (please notice: direct state access function) does work only for layer 0 (face positive x). The other layers are not uploaded and produce this GL_DEBUG error:
source : GL_DEBUG_SOURCE_API
type : GL_DEBUG_TYPE_ERROR
severity : GL_DEBUG_SEVERITY_HIGH
id : 0x3e8
glTextureSubImage3D has generated an error (GL_INVALID_VALUE)
System: Kaveri 7800 A-10 (Radeon R7, GN 1.1), Driver: Crimson Edition 15.12 (supposed to support GL 4.5 except shader version 450).
On NVidia GTX 970 with current driver the problem does not exist, and the upload works as expected.
The GL 4.5 spec does not allow to specify GL_TEXTURE_CUBE_MAP and GL_TEXTURE_CUBE_MAP_ARRAY as named textures for glTextureSubImage3D, but ARB_direct_state_access extension does.
Besides there is no DSA way upload data to a named cubemap texture unless a texture view with an acceptable target for glTextureSubImage3D is used ( should be considered as hack ).