  It has been shown by Marques and Nunez that the first $\alpha'$-correction to
the bosonic and heterotic string can be captured in the $O(D,D)$ covariant
formalism of Double Field Theory via a certain two-parameter deformation of the
double Lorentz transformations. This deformation in turn leads to an infinite
tower of $\alpha'$-corrections and it has been suggested that they can be
captured by a generalization of the Bergshoeff-de Roo identification between
Lorentz and gauge degrees of freedom in an extended DFT formalism. Here we
provide strong evidence that this indeed gives the correct
$\alpha'^2$-corrections to the bosonic and heterotic string by showing that it
leads to a cubic Riemann term for the former but not for the latter, in
agreement with the known structure of these corrections including the
coefficient of Riemann cubed.
