Cellular specific mass (in grams-dry-weight per pico liter)?
Density of a variety of cell types is rather well known. It can been measured directly by examining buoyancy (tendency to float) in liquids of known density, and also by microfluidic methods. But the results depend on the osmolality of the solution in which the cells are kept, since cells tend to "swell" (take up water) in low osmolality (hypotonic) medium.

Using a microfluidic technique, this paper reports a density of 1160 $\pm$ 1 pg/pL for E.coli at 290 mOsm, and 1139 $\pm$ 3 pg/pL for red blood cells. At comparable osmolality and using a gradient centrifugation method, this paper gives a density of 1095 pg/pL for E.Coli. So the results clearly differ a bit depending on experimental conditions (possibly the medium composition was different). For budding yeast, this paper estimates a density of 1103 $\pm$ 3 pg/pL, compared to 1113 pg/pL by gradient centrifugation.

In all cases, cells are heavier than pure water (1000 pg/pL), and larger eukaryotic cells seem to be slightly more dense. As macromolecules are more dense than water, this would suggest that eukaryotes have lower water content.