Christopher: 

Dig out all of the cinder that you can get out, lest it be a task similar to a jay filling a house with acorns in which case don't take all of the cinders out, and then go to the hardware and ask for mortar sand mix (concrete has gravel in it and since you are talking a +/- 3" hole you don't need the gravel/aggregate). Mix it up really really dry, just enough water that it will cake up in your hands (suggest rubber gloves like for dish washing) -- not mushy -- you are not setting brick or making mud pies, and then put it in the hole. Take a stick, short handle of a broom, or the handle of a hammer, and tap/pack the dry mortar into place. When you get to the top 1" or so mix up a bit of the mortar a little little bit more wet, just enough so that you can smooth it out with a butter knife or very small trowel or putty knife (cheaper than a trowel at the hardware store). Bring the mortar up to where you need it and smooth it out then leave it alone (like don't step on or in it) for at least 2-3 days... if you made it dry then it will set up fairly quickly. If you made it wet then you will be cussing already because you will have a mess to clean up. If you want to glue something down to it it is best to wait 14 days.

Mortar/masonry on wood is not the best thing, it tends to trap moisture into the wood, if you want to do the wood part with a bit of wood cut to fit it is ok... but you can also put a vapor barrier between the wood and the mortar patch... either smear the wood with rubber cement and let the cement set, or use petroleum jelly (be inventive), or kitchen plastic wrap. The separation of wood from mortar here is for the persnickety... I would just pack the dry mortar in place.

Dry mortar shrinks less than wet mortar.

Hydraulic cement has a tendency of setting up really really fast and is mixed in 1-2 cup units. It is used for things like filling holes with bolts in them or plugging a hole where water is actively flowing through it. It sets up really really fast. 

One time we had a fiasco on one of our projects, for one of our Jr. project managers, for the Plaza, where the Jr. project manager wanted the sidewalk repairs, which required an extensive thin overlayment, to use hydraulic cement. He ordered like 100 bags of the stuff. Only the Irish sidewalk mason, a really great guy that told neat stories, did not know what he was getting into. Doing sidewalks you don't usually run across hydraulic cement. 

Poor guy first thing he did was freeze up his mixer when the batch of mortar set too fast... and when he got over that episode of foul cussing he found it even more interesting that once he got the stuff laid out on the sidewalk it would set up before he could smooth it out. He had never seen any concrete like this in his life. It was a rush before some Holiday job and it all had to be chipped out and done slow after that with regular setting mortar. It was also a problem keeping the colors not looking like they were mixed in marbelized swirls. 

Needless to say he stopped doing any work for the Jr. project manager. Neither do we get asked to work at the Plaza since then. Ever since when my Irish friend does brick work for me I tell him to watch out I don't start ordering fast setting brick. 

Last I heard Seamus Mularky has terminal cancer.

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