  We introduce a variant of the multiplicative Sewing Lemma in
[Gerasimovi\v{c}s, Hocquet, Nilssen; J. Funct. Anal. 281 (2021)] which yields
arbitrary high order weak approximations to stochastic differential equations,
extending the cubature approximation on Wiener space introduced by Lyons and
Victoir. Our analysis allows to derive stability estimates and explicit weak
convergence rates. As a particular example, a cubature approximation for
stochastic differential equations driven by continuous Gaussian martingales is
given.
