  An octonionic contact (OC) manifold is always spherical. We construct the OC
Yamabe operator on an OC manifold and prove its transformation formula under
conformal OC transformations. An OC manifold is scalar positive, negative or
vanishing if and only if its OC Yamabe invariant is positive, negative or zero,
respectively. On a scalar positive OC manifold, we can construct the Green
function of the OC Yamabe operator, and apply it to construct a conformally
invariant tensor. It becomes an OC metric if the OC positive mass conjecture is
true. We also show the connected sum of two scalar positive OC manifolds to be
scalar positive if the neck is sufficiently long. On the OC manifold
constructed from a convex cocompact subgroup of ${\rm F}_{4(-20)}$, we
construct a Nayatani type Carnot-Carath\'eodory metric. As a corollary, such an
OC manifold is scalar positive, negative or vanishing if and only if the
Poincar\'e critical exponent of the subgroup is less than, greater than or
equal to $10,$ respectively.
