  We analyze the stationary spin-dependent transport through a single-molecule
magnet weakly coupled to external ferromagnetic leads. Using the real-time
diagrammatic technique, we calculate the sequential and cotunneling
contributions to current, tunnel magnetoresistance and Fano factor in both
linear and nonlinear response regimes. We show that the effects of cotunneling
are predominantly visible in the blockade regime and lead to enhancement of
tunnel magnetoresistance (TMR) above the Julliere value, which is accompanied
with super-Poissonian shot noise due to bunching of inelastic cotunneling
processes through different virtual spin states of the molecule. The effects of
external magnetic field and the role of type and strength of exchange
interaction between the LUMO level and the molecule's spin are also considered.
When the exchange coupling is ferromagnetic, we find an enhanced TMR, while in
the case of antiferromagnetic coupling we predict a large negative TMR effect.
