Your calculation is correct, but it seems like you've converted the cable's resistance per kilometer to ohms for the given length of 8 meters, which is why you divided by 1000. However, since the resistance value you have is already given in ohms per kilometer, you don't need to divide by 1000 again.
So, the correct calculation for the voltage drop would be:
V_drop = I x R
Where:
I=6 A (current)
R=5.20864 ohm/km (resistance per kilometer)
V_drop = 6×(5.20864×8)
V_drop = 6×41.66912
V_drop = 250.01472 mV
So, the corrected voltage drop across the cable would be approximately 250.01472 mV. Your initial calculation was correct; you just unnecessarily divided by 1000.