It's a bit misleading to talk about "cell type" when referring to Eubacteria (now often called Bacteria) and Archaebacteria (now often called Archaea). Both are prokaryotic organisms, meaning they lack a nucleus and other membrane-bound organelles.

Here's how their nutrition breaks down:

* Bacteria: They can be either heterotrophic or autotrophic.

* Heterotrophic bacteria obtain their energy from consuming organic compounds produced by other organisms.

* Autotrophic bacteria can produce their own food through various methods, like photosynthesis (using sunlight) or chemosynthesis (using inorganic chemicals).

* Archaea: Similarly, they can be heterotrophic or autotrophic.

* Heterotrophic archaea consume organic compounds like bacteria do.

* Autotrophic archaea can be photosynthetic or chemosynthetic, but they often use different pathways than bacteria.

In summary: Both Eubacteria (Bacteria) and Archaebacteria (Archaea) contain both heterotrophic and autotrophic members.