Thanks Alpha01 - we call it a cubical panorama. You can render the six faces of a cube directly in Bryce - 6 renders. In the Content that came with Bryce 7.1 Pro, you find under Content/Turorials/Horo Wernli/Start.html 4 methods to create spherical HDRI panoramas. But yes, you will need additional programs. A free one would be HDRShop that can do all the tricks needed. Cubical panoramas are good for converting into QuickTime Virtuality Reality movies (QTVR). However, if you need the 6 cube faces separately as LDRI, no additional program is needed.
Instead of creating a cubical panorama, you can also work with spherical ones. These can be mapped on a sphere and your scene is inside this sphere. Unfortunately, at the moment you have to use one of the 4 methods shown in the tutorials. David and I have currently a special lens in the DAZ quality assurance process and once it has passed QA, it will be available. This special Bryce lens permits rendering a 360° by 180° panorama in one go. The result can be saved as normal picture or as HDRI for IBL
Bryce does not work with sky boxes. Either angular maps (we have a lens in the store that renders directly an angular map for IBL).or spherical (lat/long) panos can be used for IBL. If your backdrop is to be LDRI, use spherical and map it spherical on a sphere. If you use the six sides of a cube on a cube, the skybox will look as a box, not as a dome.