Energy loss and power over one period?
P(t) = u(t) x i(t) is the total loss due to copper resistance, hysteresis and eddy-currents. The hysteresis loss must be calculating using the magnetization curve for the material, the current, number of turns and the material dimensions.

The magnetization curve required would be an AC magnetization curve or hysteresis loop. I believe the hysteresis loop for the specific operating frequency would be required. The material manufacturer would probably provide curves showing core loss per kilogram of material as a function of peak flux density at specific frequencies.

A core manufacturer would probably provide loss information for specific cores.

It may be very difficult to find information that separates hysteresis from eddy-current losses.