You cite the source in which you found the speech. For example, if you found a copy of the speech in a book, cite that book. If you found it in a magazine, cite that magazine. Remember that one of the purposes of citing your sources is to allow the reader to find the same information you used from the same source you used.
Some examples from the APA Style Blog are as follows:
Dr. King’s I Have a Dream speech can be found in many sources, both online and in print. For example, I found the quotation in a book titled I Have a Dream. The following example includes the correct in-text citation:
Dr. King stated, “I have a dream that my four little children will one day live in a nation where they will not be judged by the color of their skin but by the content of their character” (King, 1963/2022, p. 62).
The associated reference is as follows:
King, M. L., Jr. (2022). I have a dream. HarperCollins Publishers. (Original work published 1963)
I also found the quotation in a recording of the speech on YouTube. An example of the in-text citation is as follows:
Dr. King stated, “I have a dream that my four little children will one day live in a nation where they will not be judged by the color of their skin but by the content of their character” (Rare Facts, 1963/2017, 3:02).
The citation includes the author, year of the original speech and year the video was published, and the time stamp for the beginning of the quotation in place of a page number.
The associated reference is as follows:
Rare Facts [@rarefacts606]. (2017, November 7). I have a dream speech by Martin Luther King Jr HD (subtitled) [Video]. YouTube. https://www.youtube.com/watch?v=vP4iY1TtS3s&t=182s (Original work published 1963)