  We renormalize a six dimensional cubic theory to four loops in the MSbar
scheme where the scalar is in a bi-adjoint representation. The underlying model
was originally derived in a problem relating to gravity being a double copy of
Yang-Mills theory. As a field theory in its own right we find that it has a
curious property in that while unexpectedly there is no one loop contribution
to the $\beta$-function the two loop coefficient is negative. It therefore
represents an example where asymptotic freedom is determined by the two loop
term of the $\beta$-function. We also examine a multi-adjoint cubic theory in
order to see whether this is a more universal property of these models.
