Well without spending too much time getting the exact answer, I would suggest listing the different appliances used for a start.
1. Your body: walking to the kitchen, moving around, pouring, lifting etc
2. Energy involved originally in making that cup: How was the cup made? when? where? what materials were used?
3. Same for the kettle, spoon, coffee, sugar and/or milk if applicable.
4. Electricity used to boil the kettle
5. The body heat of all people involved in harvesting the coffee, making the cups
6. The energy used by vehicles to transport the materials used at each point along the way.
7. All the above uses of energy that are applicable to making the transportation vehicles and accessories.
8. Don't forget the roads and accessories; and the workers energy!
9. How big is the cup of coffee?
10. The factors go on
If you just want to know how much energy is used to boil a kettle: Around 0.15 KW for one filled with a cups worth of water apparently. Again there are so many factors involved.
All aside: If you want to save energy while making your coffee; don't boil more water than you need for the cup/s.