The actor took to Instagram to post a black-and-white picture of Bill and his siblings Brett and Mark, The Hudson Brothers, posing in the street.
"The Hudson Brothers.. which one is my dad Bill? One day I wanna be this cool..," Oliver captioned the post.
VIDEO: Goldie Hawn dances with son Wyatt in the street
Fans were quick to comment on the post, with one writing: "You are cooler than Bill because you're Oliver," while another wrote: "You're the coolest already." A third added: "I had such a crush on them back in the day."
The Hudson Brothers shot to fame after appearing on the Sonny and Cher Show, which resulted in them performing in their own variety half-hour series, The Hudson Brothers Razzle Dazzle Show, which ran from 1974-75.
During this time they also released a number of singles. Bill was married to Goldie from 1976 to 1982, and has had a strained relationship with Oliver and Kate for many years.
Oliver Hudson paid tribute to his father Bill Hudson
The pair were raised primarily by Goldie and her long-term partner Kurt Russell, who they affectionately refer to as 'Pa'.
In recent time, however, the siblings have spoken out more and more about Bill in a positive light. Oliver confirmed in 2018 that he had exchanged "some texts" with his father.
Bill Hudson and Goldie Hawn were married from 1976 to 1982
And in a 2016 interview with Howard Stern, Kate said of her dad: "I really do recognise whatever those issues are, it’s just something that he has to live with, and that must be painful for him, so I forgive him."
In June, meanwhile, Oliver paid tribute to both Bill and Kurt on Father's Day. Alongside three throwback photos – one of Bill, one of Kurt and one tongue-in-cheek image to his "potential" father Warren Beatty.
Oliver is incredibly close to his famous mom
The actor wrote: "It doesn’t really matter which one of these men is my father. "My Pa stepped in when I was 6 and made the man I am today..
"My Dad is half of me and as I get to know him I realize how alike we actually are.. and there’s a very good chance Warren Beatty is my actually father.. HAPPY FATHERS DAY!! #itsokaytocry."
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