Here is what LTSpice says. Note that you can think of the Current source as a 70mA dc current source in parallel with a 50ma sinosoidal current source. (Superposition theorem)
However, if you connect it to a 1Ω load, and have LTSpice compute the average and RMS values, it comes up with 70ma and 78.419mA, respectively.
Now, we know that this source should produce as much heating in the resistor as (Irms)^2/1 or 0.078419^2/1 = 0.0061945W.
If we ask LTSpice how much power is in the resistor, it plots V(A)*I(R1), the dark blue trace. Note the weird wave-shape, which results from the product of two sine waves. When I ask LTSpice what is the average of the blue trace, it comes up with the value in the second box, namely 6.1495mW... Not bad, huh.