Perchance had you tipped the mower to clean out the grass? If so , the air filter element could be contaminated. I would assume that the fuel was fresh in a new can also? For future use, just buy the regular unleaded fuel, though that would not create a no start situation.

If you just brought it take it back it should be under warranty

Check the choke.

Sounds like a fuel starvation problem. Could there be a problem with the gas cap? Not venting? Can you return it?

For those of us who are not familiar with this model, can you add some details? Does it start by primer (rubber bulb you have to push a few times) or by choke (either a position of the throttle lever if so equipped, or an automatic choke)? Like baymee said, its running out of fuel. To start with, mowers are set-up for regular gas, not premium, although one should run fine on premium. More importantly, where and when did you get this gas? I suspect water in the fuel which settled in the float bowl. But if you are using Ethanol-enhanced fuel, like E10 or E15, any moisture in the fuel stays in solution because of the alcohol.
If it were mine, I would empty the fuel tank and carburetor float bowl and refill with fresh regular gas. There probably is not a fuel shut-off valve on a Briggs engine but take a look at the starting procedure in the owner's manual anyway and make sure you're doing everything right.
Find the spark plug wire and push the terminal 'on' in case its not fully connected. Now try to wiggle the spark plug - it should not move.
Does the mower or fuel can stay outside without a cover by any chance? That's a real good way to get water in the fuel.