According to the search results, "cuk" has multiple meanings and uses, some of which are derogatory and offensive. Here are the different definitions found:

• Urban Dictionary: "To have gay sex with a stranger", "A man who lets his wife or girlfriend have sex with other men. Often the man lets her do whatever she wants and treat him like shit".
• The Globe and Mail: "A modern swear word thats as dirty as the old ones". It is short for "cuckold," meaning a man whose wife has sex with another man. In recent years, "cuck" has also become synonymous with a genre of porn in which a man (usually white) looks on as a man or men (usually black) have sex with his wife. Its use in a political context has become a racist/sexist slur against white male liberals who are seen, in far-right circles, as traitors to their race and gender.
• Wiktionary: "I pierce (with a sharp, thin object, needle, thorn, stinger, prickle etc)", "I tease, provoke (with words or gestures)".

It is important to note that the use of "cuk" as a derogatory term is offensive and should not be used.