What size cable to run 8kw shower 50 meters from main supply?

8000 watts divided by 240 volts equals 33.3 amps. If using NM cable indoors, Table 310.16 of the NEC says #8 wire is good to 40 amps. However, since this is a heating application which would qualify under "continuous duty" classifications(3hours or more of run time), then you figure it as 125%. This would in turn bump you up a wire size to #6. 33 amps times 125% equals 41.6 amps. Voltage drop would not be an issue even with #8 copper.