If you read a lot of secondary fantasy, then you're probably familiar with the prevalence of history, legends, and mythology in these types of stories. Mythology can play many roles in fantasy: it can explain the origin of humanity and magic; it can show how (or whether) religion plays a role in society; it can act as a metaphor for cultural values. Etc.
I'm currently reading a novel where it seems like every other chapter, they are telling a new story of some legendary hero or phenomenon. Could I repeat any of it back to you? Nope. Not unless I opened the book to those particular pages. Why? Because a) there's too much of it, and b) none of it involves characters I know or care about. If you're asking me to remember a huge chunk of what seems like irrelevant information, there had better be a good reason for it--and even if there is a good reason, you should try to limit how much of it goes into your story.
Here are some good guidelines for incorporating mythology:
1. The mythology is only there to enrich the worldbuilding: Even if mythology isn't directly related to the plot, it often adds a sense of realism and culture to the world. If this is the case, give it to your readers in brief snatches--names and sentences interspersed among the story.
2. The myth is only relevant to this particular scene: Perhaps your characters are visiting an important historical landmark. Or maybe one character is using this myth in a metaphorical way to advise or warn one of the characters. In this case, I would limit the story to a paragraph. (If it's a particularly entertaining story, you can use two paragraphs.)
3. The myth is crucial to the plot of the story: If the characters are sitting around the campfire, listening to a story, then that story had better be important--no, indispensable--to the plot. Think about A Game of Thrones--most of the mythology is given in bits and pieces, but the history of the Tagaryens and their dragons are given a full page or two of uninterrupted narration. That's because it's important for readers to understand the potential power of dragons--something that could be major foreshadowing for later in the series. Thus, only if a myth is truly important should you dedicate half a page or more of explanation. However, even this should be done sparingly. A good guideline is no more than one info-dump myth for every 300 pages of plot. (The only good exception to this rule is A Hundred Thousand Kingdoms, but that's only because the gods are active characters in the story.)
Note that these guidelines also (read: especially) apply to songs. I don't care what Tolkien got away with. How many of the songs in The Lord of the Rings do you actually remember?
Most of your readers do not have robot memories. Hell, many of us have a hard enough time remembering to water the garden. It is unfair of you, as a writer, to tear your readers away from the plot and expect them to remember a bunch of information that plays no role in the story. If that unnecessary myth is truly as awesome as you think, save it for a supplementary encyclopedia, or better yet, a different book.