I had a female dubai roach in a cage all by itself for eight months. I went to clean the cage and discovered she had given birth to several babies. How is it possible that she gave birth with no male.

I did not find a specific authoritative reference that stated that the dubia roach is parthenogenetic, however, there is a possibility that dubia roaches, Blaptica dubia, don't need males to reproduce, which is known as parthenogenesis. There are male dubia roaches, and I surmise that dubia roaches are sexual, but in some insect species, if you raise a female by itself, they can do without, which is known as being facultatively parthenogenetic, which means that when forced or at will, the species can breed without males. How cool is that, or not.

Parthenogenesis is an asexual reproductive strategy. A sexual strategy that insects use, that might explain your experience, is that some female insect species store the "gift" (nudge, nudge) from the male for later use in her spermatheca.

(I did find a reptile blog, where someone stated that dubia roaches are parthenogenetic, but I wouldn't consider a blog any more definitive than the non-definitive answer given here. I did find a lot of scientific references to parthenogenesis in cockroaches, but nothing specific.)

It is really hard to explain how parthenogenesis works, but it has to do with cell division - meiosis, mitosis, diploid, haploid, genetics stuff.

Here is an important information about the potential danger of raising exotic animals that could become pests. Keep nature, native:

Greg's Exotic Inverts