Unless your cable is VERY poor (or damaged, which is common) , it won't matter whether you're using the shipped cable or an aftermarket usb3 or usb2 cable. The defining factor is nearly always the power source. I've used bricks that supply .6A up to 2.1A. The phone will never absorb 2100mA at charge time (according to Galaxy Charge Current), but it will well exceed 1000, and sometimes go up to 1800.
As I said before, make sure your charger has more muscle.
Think of it another way: It doesn't matter how big your pipe is if you're not putting any water in it.
Battery is 2800mAh. In the best case, a <1000mA charger will cause the phone to take a 500mA charge current, which means that (2800mAh/500mA)=5.6hours. This would be with the phone off, and the charging producing zero loss (which is not possible). let's assume 80% charging efficiency and go with the burn rate for ULP mode, which is about 39mA/h. Start charging at 20%, which is when you get your first nag. Charge time would be (2800 mAh * 0.8) / (((500 mA) - (39 mA)) * 0.8) =6.1 hours. Now, contrast that with your 2.1A charger, which will get the job done, assuming a current limit at 1800mA, as I have observed, in (2800 mAh * 0.8) / (((1800 mA) - (39 mA)) * 0.8) =1.6 hours
Mark