The decay of B mesons can be described in the Heavy Quark Expansion as the decay of a free bottom quark plus corrections which are suppressed by powers of $1/m_b$. The focus of this contribution will be on the calculation of the NNLO corrections to semileptonic decays of a free bottom quark including a non-vanishing charm quark mass. For the semileptonic decays we obtain an analytic result by solving differential equations and fixing boundary conditions in the limit of a heavy charm quark. Our analytic expression can be compared to previous known results obtained via expansions in the mass ratio $m_c/m_b$. In a second approach we calculate precise numerical expansions of all master integrals with the help of differential equations which can describe the whole parameter space from $m_c/m_b=1$ to $m_c/m_b=0$. This calculation serves as a preparation for the nonleptonic $B$-meson decays, where the same techniques as in the semileptonic decays can be used.