You should fill the cores with grout and not mortar (there is a big difference). You can go all 6 courses in several lifts as long as you bring it up slowly and rod through the last lift and into the lower lift. This way you have nor "cold joints" and have a continuous grout cell that should be topped off after and hour or so as the grout consolidates and the excess water is slowly absorbed by the block.
Why use the old fashioned 3 core block? They are hard to get in the civilized world. Two core block with flush ends are better and easier to grout. In real construction they usually use an "H" block (open ends and one web of a "double H block" with open ends and two webs to minimize the amount of grout.
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