How to calculate power loss & voltage drop in three phase power cables
... the manufacturer datasheet specifies the resistance in ohm/km (R). Does this imply the resistance per conductor core or is it for all the three cores added together?

The resistance will be per conductor core. For a twin cable you might see resistance specified &quot;per km loop&quot; which would mean the out and return resistance.
Power loss is simply \$ I^2R \$ for each cable. It doesn't matter what the voltage of the circuit is or what the load is - resistive or reactive.
Ignoring inductance, voltage drop in each conductor will be simply \$IR\$ where \$R\$ is the cable resistance.
If you wish to take inductance into account then you must calculate the cable impedance. This will depend on conductor size spacing and spacial arrangement. I this case the voltage drop on each line is given by \$ V = IZ \$ where \$Z\$ is the line impedance.