Drake, 02 Academy, Glasgow

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"It's been one of the greatest experiences of my life, playing my first international show for you," said the Canadian actor-rapper Drake, towards the end of his set, before pointing out that unidentified timekeepers were warning that he had run over. "I waited my whole life for this," he said, "so if they wanna fine me, if they wanna penalise me, I don't care." It was only half-past ten, though, so there seemed little danger of his turning into a pumpkin.

Aubrey Drake Graham talks the talk, but there is an air of controlled professionalism just below the surface. This is not surprising, given that the 24-year-old Torontonian made his name as an actor, most notably in the teen drama Degrassi: The Next Generation. His latest role, as a No 1 album artist in the US and Canada with last year's Thank Me Later, has been played to perfection, featuring collaborations with Kanye West, Eminem, Lil Wayne, Nicki Minaj, Timbaland and Rihanna. (The last, "What's My Name?", provided his biggest hit.)

Possibly due to the postponement of planned UK dates around the time of its release, Thank Me Later was not so successful here. The positioning of this debut British tour so close to the New Year, then, suggests that Drake is keen to build a following before the release of his second album in the spring. This was a gig which made an impression. It was not always a good one, but it staked his claim as an arena-filling artist to watch in 2011.

His entrance, featuring a cool strut on to the stage under the amber glow of a video-screen sunrise and a modern take on the James Dean uniform of scruffy denims and black leather jacket, was designed to get his female fans onside. "Forever" and "Up All Night" were serviceable big-room hip-hop openers, giving way to a lazy, top-down r'n'b groove through "Unstoppable" (first line: "I'm Drizzy and I ain't perfect") and the staunch and heartfelt meditation on fame that is "The Resistance".

The show had been enjoyable, if not mindblowing, when a series of slips into tired rap orthodoxy threatened to derail things. "Successful" came with musings that it was all about the "money and the cars/ cars and the clothes/ the hos... especially the hos"; "Every Girl" featured the charming line "I just can't pick one so you can never say I'm choosy"; and "What's My Name?" was prefixed by a giggling, teenage-boy description of how Drake liked to "treat" a girl in bed.

Such sentiments sit somewhere between dumb and downright sleazy, and they cheapened the many highs of the show. "Bollywood Flow" and "Shut it Down", for example, exercised some of the futuristic electro nightclub glamour that fans of Kanye West will know, while the joyous "Best I Ever Had", and particularly a wonderful coda to "Miss Me" which saw Drake spend five minutes giving personal shout-outs to dozens of individuals in the crowd, were lovable and inclusive set pieces.

After that rebellious turn against whoever was tapping their watch in the wings, the anthemic "Over" cascaded through an array of positive lyrical messages, a mighty turn from the full backing band, flaring neon lights and a flash of fireworks at the finale. For a show which wasn't without its sour moments, it made for a sweet ending.