I am currently working on the creation of Planet Generation mainly for fun and hope that some planetary back planets will eventually appear. I use a cube that has been converted to a normalization sphere. 
In this image, the landscape is not yet textured. This is just a height map render. However, this is not my problem. When creating a sphere from a cube, you are left with 6 faces bent to the shape of a sphere. Therefore, I do not have the latitude and longitude that can be used to wrap a spherical height map around the relief. I am currently using Cube Mapping. However, this caused several problems, as you can see:
where my problem becomes apparent. The problem is that the sphere still has a cube topology. I need to create a height map for each person. I am currently using Libnoise for a height map, and this is where the big problem starts. I can either export it as a spherical height map - mdash, which would be useful if I had a sphere, or I can use planar height maps, which should be displayed on all 6 faces. However, due to how mapping works. I can get 3 faces to line up around the middle and be seamless, but the last height map will not join the first because the Lib noise uses borders and creates a grid of coordinates.
A sphere is created like this:
for(int i = 0; i < vertices.size(); i++) { glm::vec3 oldVec = vertices[i]; glm::vec3 newVec = glm::normalize(oldVec); vertices[i] = newVec * glm::vec3(500, 500, 500); }
The rationale for this can be seen here .
However, the structure of the sphere will simplify the implementation of Lod in the form of Quad-Ttee later. Is there anyway I can create a cube height map with LibNoise? Or is there something I can do to make the sphere use a spherical height map?
I figured out how to render it using Sphere Maps, but that will not work when I come to use the square tree. However, it gives good results, for example:

So, I pretty much need to know how to alternate the noise in a cube map. Either in Libnoise or in the vertex shader.