Please let me ask you a simple question.
Is it possible to use GL_DEPTH_COMPONENT format with GL_TEXTURE_CUBE_MAP_ARB?

I want to make a depth cube map…

According to the OpenGL specification, it should be possible. Unless I overlooked something.

void TexImage2D( enum target, int level,
int internalformat, sizei width, sizei height,
int border, enum format, enum type, void *data );

is used to specify a two-dimensional texture image. target must be one of … or one of TEXTURE CUBE MAP …
The other parameters match the corresponding parameters of TexImage3D.

I think I actually saw some applications of depthmapped cube maps here and there so, I guess it’s possible.
Take this with some salt however.