  We consider algebras of $m\times m\times m$-cubic matrices (with
$m=1,2,\dots$). Since there are several kinds of multiplications of cubic
matrices, one has to specify a multiplication first and then define an algebra
of cubic matrices (ACM) with respect to this multiplication. We mainly use the
associative multiplications introduced by Maksimov. Such a multiplication
depends on an associative binary operation on the set of size $m$. We introduce
a notion of equivalent operations and show that such operations generate
isomorphic ACMs. It is shown that an ACM is not baric. An ACM is commutative
iff $m=1$. We introduce a notion of accompanying algebra (which is
$m^2$-dimensional) and show that there is a homomorphism from any ACM to the
accompanying algebra. We describe (left and right) symmetric operations and
give left and right zero divisors of the corresponding ACMs. Moreover several
subalgebras and ideals of an ACM are constructed.
