If you accumulate 100 identical spheres how many will end up on the surface?
Experimental approach
Here are 100 marbles in a polyethylene bag:

If a marble touches the bag, it is counted as being on the surface. I did not count, and the bag was not perfectly round. A balloon might be better.
Theoretical approach
This works for large $N,$ and the result is as Ivan predicted (from scaling arguments in 2D and 3D, I would imagine). We neglect the packing defects in the bulk, and treat the surface as having no curvature and no defects. The maximal packing density of spheres is well-known by chemists,
$$P_\mathrm{3D} = \frac{π \cdot \sqrt{2}}{6} = 0.74046\ldots\tag{1}$$
The maximal packing density of circles is less well-known on this site, but you can look it up on Wikipedia:
$$P_\mathrm{2D} = \frac{π \cdot \sqrt{3}}{6} = 0.90687\ldots\tag{2}$$
If you have $N$ marbles with radius $r$, you can estimate the radius $R$ of the enclosing sphere, get its area ($4 \pi R^2$), and calculate how many circles (of area $\pi r^2$) fit in that area. The resulting expression scales with $N$ to the power of two-thirds, as Ivan said:
$$N_\mathrm{surface} = 4 \cdot P_{\mathrm{2D}} \cdot \left(\frac{N}{P_{\mathrm{3D}}}\right)^\frac{2}{3}\tag{3}$$
For example, for a million spheres, about four percent are on the surface. For a single sphere, all are on the surface. The expression for $N = 1$ yields $4.4$, pretty bad. For $N = 100,$ it yields $95.2$ That is a not a bad estimate; from the experimental approach, I see more than $30$ marbles on the surface, and the picture only shows one side.
Approximating a sphere with a cube
If you have 125 spheres that pack in a primitive cubic fashion, you would have a cube with 5 spheres in each direction. The top and bottom, right and left, front and back layer would be on the surface, leaving a 3 by 3 by 3 cube in the center. So 27 spheres would be on the inside and the remaining 98 would be on the surface. When we take those same 125 and pack them tighter and such that they fit in a minimal sphere, the surface area would get smaller, and the packing on the surface would get denser, leading to a similar fraction of spheres on the surface.