The drain cap under the sink may be passed the clog. 2 kettles of water I would assume may amount to a gallon or so. This means the clog is not too far. Remove the p-trap and look directly and feed the snake into the pipe.
You can also purchase a pressure water feed that goes into that drain pipe. It fits on a gardon hose, feed it in that pipe and Turn the water on The mechanism is rubber and it responds to the pressurized water and it expands against the wall of the pipe and blust off whatever is there.

I hope this helps. Take care.

The drain cap under the sink may be passed the clog. 2 kettles of water I would assume may amount to a gallon or so. This means the clog is not too far. Remove the p-trap and look directly and feed the snake into the pipe.
You can also purchase a pressure water feed that goes into that drain pipe. It fits on a gardon hose, feed it in that pipe and Turn the water on The mechanism is rubber and it responds to the pressurized water and it expands against the wall of the pipe and blust off whatever is there.

I hope this helps. Take care.

Did you take the P trap out? See pic?