You asked:

is robin thicke the son of allen thicke

Yes. Robin Thicke is a son of Alan Thicke.
Alan Thicke
Alan Thicke

Alan Thicke (born Alan Willis Jeffrey on March 1, 1947 in Kirkland Lake, Ontario, Canada), the Canadian actor, songwriter, game show host and talk-show emcee

Robin Thicke
Robin Thicke

Robin Charles Thicke (born March 10 1977), the R&B and soul singer, songwriter, musician, composer, and occasional actor

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