Realtime cubemap that respects rotation?

Is there a way to generate a realtime cubemap that respects the rotation of the camera?

For our project we need to be able to generate a cubemap from a camera's location. This camera is moving through a room and rotates.

Camera.RenderToCubemap seemed perfect for this. However, this function doesn't seem to respect the rotation of the camera and only seems to use its position.. if I rotate the camera, the generated cubemap doesn't rotate with it.

We need to be able to do this so that we can use this generated cubemap for further projections.

I thought about manually linking 6 camera's to the main cam and generate the render textures from that to put in a cubemap, but I don't even know where to start with that.. CubeMap.SetPixel on every camera for every slot?

Hopefully someone has some experience with this?