Gentile-Sheva Mitzvos Bnei Noach:[1]

Although Gentiles were not commanded in the laws of honoring their father and mother as part of the seven Noahide commands[2], nevertheless, they are practically obligated in showing some degree of reverence to their parents.[3] [Thus, it is forbidden for a Gentile to shame, curse, or hit his parents. Likewise, they are obligated to listen to their instructions, although they are not obligated to feed and clothe them.[4]] A gentile who honors his parents receives reward even if he is not obligated to do so from the letter of the law.[5]

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[1] Pesakim Uteshuvos 241:7; Encyclopedia Talmudit Erech Kibud Av Vaeim Vol. 26 p. 375

[2] Omitted from Sanhedrin 56b; See Kiddushin 31a which implies that a gentile is not commanded in the Mitzvah of Kibbud Av “Ula taught: The extent that one must go to honor one’s parents can be learned from a certain idol worshiper from the city of Ashkelon by the name of Dama the son of Nesina. The sages came to him with a business offer to purchase an item of his that would give him 600,000 gold coins as profit. However, since the key to retrieve the item was under the head of his father who was sleeping, he could not sell the item, as he did not want to awaken his father and cause him pain. Rebbe Eliezer taught the same story, however adding that the item that the sages desire to purchase was a precious stone for the Ephod, and that the next year G-d rewarded the Gentile by having a red cow born to his heard. When the sages approached him regarding the sale of the red cow, he replied that although he could request any money in the world, he only request the amount of money that he lost from not selling the precious stone the previous year due to his desire to honor his parent. Rav Chanina stated that if someone who is not even  commanded in the mitzvah receives such reward all the more so will be the reward of one who is commanded and does so.”; Nazir 61a; Rabbeinu Chananel Ben Shmuel and Rabbeinu Baruch on Kiddushin ibid; Rabbeinu Peretz on Nazir ibid; Beis Hillel 241; Yad Avraham 241; Zekan Aron 2 Y.D. 87; Yad Shaul 241:4; Shaareiy Deiah 241:9; Divrei Yatziv Y.D. 127; Likkutei Sichos 5:147 and 154-155; 313-314; 406; Vol. 36 p. 95; Encyclopedia Talmudit ibid footnotes 63-64

[3]  Implication of Michaber Y.D. 241:6 who says that a convert is obligated to respect his parents being that he was obligated to do so prior to his conversion [Hagahos Rav Akiva Eiger 241; However, see Likkutei Sichos Volume 5 p. 154 footnote 38 that from here we learn that he is obligated in not shaming his father and not that he must also respect]; Implication of Megillah 17a that Yaakov as punished for the 22 years that he did not serve his parents [See Likkutei Sichos p. 154 footnote 32]; All Geonim who list Kibud Av Vaeim as part of the laws a gentile is to keep [brought in Encyclopedia Talmudit ibid footnote 67-68]; Rashi end of Parshas Noach that Avraham was required to fulfill Kibud Av and 9:23; Zekan Aron 2 Y.D. 87; Igros Haperi Megadim Igeres 3:20, brought in Hagahos Rav Akiva Eiger 241:9; Nachal Eshkol 2 p. 126; Keli Chemda Yisro 7; Meiah Shearim Shaar 51; Igros Moshe 2:130; Encyclopedia Talmudit ibid footnotes 66; Likkutei Sichos 5:51 footnote 34 that Kibud Av existed before Matan Torah and therefore Sheim was required to assist his father Noah in assisting with feeding the animals in the ark; Likkutei Sichos 5:142 footnote 5b; p. 147; p. 154 that at the very least they were commanded against shaming their parents and therefore we find that Cham was punished for shaming his father [See Bereishis Raba 36:6; Pirkei Derebbe Eliezer 23; Rashi 9:23] and that is also why Lavan was considered wicked for the fact that he answered prior to his father Besuel [see Rashi Chayeh Sarah 24:50] p. 160-161 that gentiles were only commanded in a certain degree of honoring their parents and not to the full extent of a Jew after the giving of the Torah

The reason: This obligation is due to that a) the Gentiles have accepted upon themselves to honor their parents despite not being commanded in it. [Geonim ibid; Zekan Aron 2 Y.D. 87; Igros Haperi Megadim Igeres 3:20 and Poras Yosef, brought in Hagahos Rav Akiva Eiger 241:9; Likkutei Sichos 5:147] b) The Gentiles are slightly obligated in honoring their parents in order to show their gratitude and not cause a desecration of G-d’s name. [Keli Chemda Yisro 7; Igros Moshe 2:130; Likkutei Sichos Volume 5 p. 160 footnote 67-68 and page 407 based on Yerushalmi Peiah 1:1] c) The Gentiles accepted this command upon themselves when the Torah was given. [Meiah Shearim Shaar 51] d) Any matter that is required for the settlement of the world is an obligation even upon Gentiles and is included in the command to civilize the world and establish courts of justice [i.e., Dinim]. Hence, even gentiles were commanded in a certain degree of honoring their parents but not to the full extent of the Jewish people after the giving of the Torah in which case honoring one’s parents became a full independent command. [Likkutei Sichos Volume 5 p. 160 and p. 406 based on Ramban and Yerushalmi ibid; Nachal Eshkol ibid; Keli Chemda ibid] e) Any matter which the human mind obligates as a part of morality and civility is obligatory upon gentiles. [Hakdamas Ran Gaon Brachos; Yad Efraim 4 p. 170; Likkutei Sichos Vol. 36 P. 95 footnote 47] See Encyclopedia Talmudit ibid p. 376 footnote 67-75; See Likkutei Sichos 36:96 that there are two aspects in the mitzvah of honoring one’s parents, one an intellectual moral aspect which is between man and his fellow, and a second which is between man and G-d, as through honoring one’s parents one honors G-d. The Rebbe there explains that only the former aspect is relevant to Gentiles, while the latter aspect is only relevant for Jews, as only by Jews is the infant light of G-d united with their bodies, and hence does honoring them not consist of idolatry, in contrast to Gentiles in which honoring them with consist of Shituf.

[4] Keli Chemda ibid

[5] Kiddushin ibid

[6] See Targum Yonason Ben Uziel Vayishlach 32:12; Bereishis Raba 82:14; Devarim Raba 1:5; Zohar 1:146; Likkutei Sichos 36:91 footnote 10.

[7] See Tanchuma 8 and Pesikta Rabasi 23 that Moshiach cannot come until Esav receives his reward for honoring his parents.