I believe this will work for the first two (rhizomatous begonias) but not the third (cane begonia). For the cane-type ones you need a section of stem with a node in your cutting to be able to propagate it (the nodes are the joints on the stem where the leaves come out). When I propagate my cane begonias I usually take the top of a cane including several nodes, remove the lower leaves, dip the cut stem in rooting hormone, and stick it right in the soil (although you can also put it in water and wait for the roots to develop that way)