I try to enable writeback:

   sudo echo writeback > /sys/block/bcache0/cache_mode

it returns the error

   bash: /sys/block/bcache0/cache_mode: No such file or directory

You're confusing bcache0 with bcache0/bcache

    echo writeback |sudo tee -a /sys/block/bcache0/bcache/cache_mode

will work.