It’s tempting to think that the answer is 125, as the space is the volume of 125 unit tetrahedrons, however tetrahedrons cannot pack without leaving gaps.

To the best of my knowledge the most you can fit in is 65:

On the bottom level you can fit 25 pointing upwards and 6 pointing downwards; on the next level up you can fit 16 pointing upwards and 3 pointing downwards; on the middle level you can fit 9 pointing upwards and 1 pointing downwards; on the next level you can fit 4, and a further 1 at the very top, giving a total of 65.