While there are no physical depictions of Cxaxukluth, as an Outer God it can be assumed that his true form is something completely unimaginable to the mortal mind.
The offspring of Azathoth through the process of spontaneous fission, Cxaxukluth came to our solar system with his family from the green binary star system of Xoth. Once here, these horrors settled on the planet Yuggoth; however, Cxaxukluth's cannibalistic tendencies soon scared off the rest of his clan, who proceeded to migrate to Earth. Mercifully, their patriarch elected to remain on Yuggoth, where he resides to this day, periodically causing a mass exodus of the Mi-go from their colony on the planet whenever he makes his vile presence known above the surface.
There is speculation that Cxaxukluth split into the twin entities of Nug and Yeb in order to produce offspring with itself, but speculation is all that this is.