A historic statue outside Sydney’s Queen Victoria Building has been graffitied by a vape-loving skateboarder in broad daylight.

The man, clad in a colourful jumper adorned with an eye, painted ‘vape don’t rape’ and ‘tit 4 tat’ on a statue of Queen Victoria about 4pm on Wednesday.

The statue, originally from Ireland, is more than a hundred years old and has been at the entrance to the Queen Victoria Building since the 1980s.

Police say they’ve also received reports of similar graffiti in other parts of the CBD and are investigating whether the incidents are linked.

They are appealing for anyone who may have seen the man in his 20s to come forward.

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AAP