  Let X be a Calabi-Yau threefold and \mu the symmetric trilinear form on the
second cohomology group H^{2}(X,\Z) defined by the cup product. We investigate
the interplay between the Chern classes c_{2}(X), c_{3}(X) and the trilinear
form \mu, and demonstrate some numerical relations between them. When the cubic
form \mu(x,x,x) has a linear factor over \R, some properties of the linear form
and the residual quadratic form are also obtained.
