We report on first-principles calculations for metallic carbon nanotube superlattices N͑12, 0͒ / N͑6,6͒ with N =1-4. Although the calculated band structures show a good overall agreement with the results of the simpler tight-binding -electron approximation, electron interaction and correlation effects strongly modify some peculiar flatbands, previously found within a tight-binding approach ͓W. Jaskólski and L. Chico, Phys. Rev. B 71, 155405 ͑2005͔͒. In the ab initio approach, these bands are no longer dispersionless, much closer to the Fermi level, and are always nondegenerate, in contrast to former tight-binding results.