What is the appropriate noun-word or other expression for the disposable left-over or remains of sugar-cane after we chew and suck up its' juice. If I call it "cuds" does it communicate right?. Any other better word than "cuds"?.
"Cud" is specific to ruminants (cows etc.) and implies that the plant material has been mixed with the contents of the stomach before being chewed again. Humans don't do this, so I would not use this word.
Technically, these remains are called "bagasse": https://en.wikipedia.org/wiki/Bagasse
However, that is very specific vocabulary and would be unfamiliar to most people. Also, it typically refers to what is left over after the cane has been machine-crushed, not chewed by a person.
I don't know of any common word that refers to what you want. Perhaps there is one among the cultures where sugar cane is grown, but if so it is likely to be very local in use and not in English.
For informal use, I would suggest something like remains, pulp, fiber, etc.
"Having sucked the juice from the wad of cane, he spat out the pulp..."