Working on it...

 Transferring 10 MB of data uses about the amount of energy in a AA battery which is 0.0039 kWh
Here are the top ten viewed YouTube music videos and the number of times they were viewed (while I compiled this tonight).

Song Title	Artist	Uniform Resource Locator	Number of Views
Despacito	Luis Fonsi ft. Daddy Yankee	https://youtu.be/kJQP7kiw5Fk	6965149726
Baby Shark	PINKFONG	https://youtu.be/XqZsoesa55w	6555048616
Shape of You	Ed Sheeran	https://youtu.be/JGwWNGJdvx8	4974976171
See You Again	Wiz Khalifa ft. Charlie Puth	https://youtu.be/RgKAFK5djSk	4721137015
Uptown Funk	Mark Ronson ft. Bruno Mars	https://youtu.be/OPf0YbXqDm0	3945458571
Gangnam Style (강남스타일)	PSY	https://youtu.be/9bZkp7q19f0	3782347210
Sorry	Justin Bieber	https://youtu.be/fRh_vgS2dFE	3338412458
Sugar	Maroon 5	https://youtu.be/09R8_2nJtjg	3281040028
Roar	Katy Perry	https://youtu.be/CevxZvSJLk8	3172242295
Thinking Out Loud	Ed Sheeran	https://youtu.be/lp-EO5I60KA	3072397098

 The average video play time is ~ 4 minutes which equates to about 40 MB of data transfer per video per view.
The total number of views for the 10 songs above is 43808209188.
This translates to 683408063.3328 kWh of energy for the data transfer alone. 

 I'm just warming up.  Thanks for the confidence and the pressure JJG, it will help me to achieve the optimal level of arousal required to complete my mission.

 Wait, should I even bother to include data transfer for pool mining or just the CPU/GPU/FPGA/ASIC power required for hashing?

  Don't worry @Hueristic.  I'll use the network hash rate in my calculation to ensure the energy usage from all miners is included.