Just a couple more thoughts. Concrete usually has aggregate ( smaller stones ) mixed in with the sand and cement. The brown blotches on your rock appear to be lichen stain or difused granite type material, rather than defined edged stones as would be expected with concrete.

It is possible to make concrete with finer bulking agents such as cinders, but this concrete is even more crumbly and not as strong as normal concrete. I would not expect fine aggregate concrete ( or any concrete ) to break from the  edges in shards as per your photo, but rather break in small random blobs. The only time you might achieve that effect with concrete is if the edges where broken while the concrete was still partially set, causing flakes of the wetted exterior coating, while the inside was still uncured. This would leave a more grainy feel to the exposed sections, rather than a hard shiny finish.

Although we are only working from one photo and cant handle to stone, my vote is definately for an aboriginal axe head.