You didn't say it was an ionized cloud you said it was a solid.. 1 cm cu. which 1 cm ^3 is 1000mm^3
Thats 3 decimal places there.....Your math is really bad....Almost as bad as my writing! 
That being said...
I understand that electrons have huge orbital paths around the nuclei containing protons... and atoms do not go into each others space....
But they are to small to see, and I have worked with microscopes for silicon wafer handling inspection magnifications of 100,000x ...
and have seen 100,000 nand gates in one layer of a chip in a square mm on a single layer....I'm certainly not looking through an electron microscope, just a plain old leitz glass industrial clean room microscopt.
So you claim of a few thousand particles is what makes up cm^3 or even a cubic mm^3 ....
IS SPECIOUS ....
Where do you teach? Obviously not college...