  We present closed form expressions for the ranks of all cohomology groups of
holomorphic line bundles on several Calabi-Yau threefolds realised as complete
intersections in products of projective spaces. The formulae have been obtained
by systematising and extrapolating concrete calculations and they have been
checked computationally. Although the intermediate calculations often involve
laborious computations of ranks of Leray maps in the Koszul spectral sequence,
the final results for cohomology follow a simple pattern. The space of line
bundles can be divided into several different regions, and in each such region
the ranks of all cohomology groups can be expressed as polynomials in the line
bundle integers of degree at most three. The number of regions increases and
case distinctions become more complicated for manifolds with a larger Picard
number. We also find explicit cohomology formulae for several non-simply
connected Calabi-Yau threefolds realised as quotients by freely acting discrete
symmetries. More cases may be systematically handled by machine learning
algorithms.
