Calculation of transmission loss of a power plant
Yes, your engineering is correct, the power loss in the cable is \$I^2R\$. 

This calculation is a good demonstration for why nationwide power distribution needs transmission voltages in the 100s of kV, and even a district tends to use 10s of kV, to control the power loss in the distribution cables to be reasonable, or avoid unaffordable conductors with the cross section of tree trunks.