Shakyamuni Buddha never taught anything about his birth, which has become the focus of fan fiction at the level of Jesus and Moses. Legend has it that he was born from his mother’s side while she held a tree branch, and immediately stood up to point up and down, saying,
I am the highest in this world; I am foremost in this world; I am the best in this world; this is the last birth; there is no further becoming here. (Pali canon, “Lion’s roar”)
Below the heavens and above the earth, I am the only Honored One. (Inaccurate translation from Chinese 天上天下唯我独尊)
Where is the Buddha originally quoted as saying "On heaven and earth, I alone am honored"?
The Mahāpādāna Sutta (D.ii.12-15) and the Acchariya-bbhuta-dhamma Sutta (M.iii.119-124) contain accounts of other miracles, which attend the conception and birth of a Buddha. Later books (e.g., J.i.) have greatly enlarged these accounts.
Including prophecies that he would become either a Chakravarti Raja or a Buddha.
Nevertheless, Buddhists all around the world celebrate his birth at Wesak/Vaisakha, on or near the full moon day of the fifth month in whichever calendar they like. The next full moon in the Western calendar will be May 23, so many Western Buddhists celebrate it on the weekend before that.