Where can one find a detailed analysis by Carl Jung of the novel The Black Cloud by Fred Hoyle? Under what title, in what year, and in what resource was it published?
In the biography on Carl Jung titled Carl Gustav Jung: A Biography, author Frank McLynn notes that Jung became extremely fascinated by society's obsession with extraterrestrials, an obsession that started in the 1950s. He saw the obsession as an unconscious "post-nuclear guilt and paranoia." He further spent a great deal of time analyzing the phenomena, leading to an essay on UFOs that he published in 1958. Soon after, Jung read and developed a deep appreciation for Fred Hoyle's science-fiction novel The Black Cloud. Jung particularly saw the black cloud in the title as representing man's unconscious paranoia that stems from mankind's guilt of having developed and set off the nuclear bomb.
Hoyle's book led Jung to develop further thoughts about UFOs, ultimately leading to the publication of Jung's book Flying Saucers: A Modern Myth of Things Seen in the Skies. It is in this book that he speaks in detail about The Black Cloud, since it was his source of inspiration. So, it's possible what you are looking for is in Jung's book Flying Saucers.
Jung also speaks again of The Black Cloud in his book Abstracts of the Collected Works of C. G. Jung, particularly in chapter 15, "The Spirit of Man, Art and Literature." So it is possible that what you are looking for can be found in that book and chapter.