paper mulberry
榖 refers specifically to the paper mulberry tree, a plant used in papermaking.
榖 combines 木 (tree) with a phonetic component that historically included 殳 and the upper elements. The right side likely contributed the sound while 木 indicates a type of tree.
The left side is 木 (tree). The right side looks like a complex tool for beating fibers. Picture a paper mulberry tree being processed into paper: the tree provides the bark, and the tool-like shape on the right represents the beating process.
For コク, imagine a cook using paper mulberry bark to make a special paper: cook -> コク, and the cook works with the tree.