How to calculate electrical energy consumed?
You've calculated correctly. But, it doesn't use a constant 500W like some light bulb, it greatly depends on the load. For a reasonable estimate, we can use some equations assuming that it uses a constant 500W, like a light bulb. And this is assuming 100% efficiency.

\$\frac{500W × 13min}{60min}=108.3Wh\$

But this is not a fair setup, it will consume \$108.3Wh\$ if it's working as much as it possibly can, full speed and full load for 13 minutes. 

If you want a fair setup, then place 2 wattmeters between the power supply and the motor and measure correctly. And if you want the energy consumed, the Wh, then connect some mcrocontroller and integrate the power. That will give you a perfect estimate. 

You can get away with only 1 wattmeter if you also got the ground line, but that is also assuming that the coils in the motor are symmetric. aka identic impedances. In real life, that never happens. So with only one wattmeter you might be off by a couple of %. 

-- Sorry for the wrong answer I made first, I'm pretty rusty.