Soldering a high-power cable to a PCB
From the photos it looks like you are desiging a brushless driver for RC car , the RC car motor and batteries are sized for short pulses of high current and not continuous , so the limit in your case is not the PCB traces .

BUT anyway i will present some of the methods used :


Using a High or VERY high thick copper PCB (4oz to 20oz) probably the most expensive and not available anywhere
Copper bus bars welded or screwed into PCB 
Copper wires soldered into PCB 
Solder wick/Braid , this is my favorite since it doesnot required the amount of heat that the previous methods used which leads to permenant PCB bend.












MY Preferred Solution :



EDIT: Added PCB termination 

Wurth Electronics power elements 



or lugsdirect PCB Wire Connectors