  We consider the partition function for Euclidean $SU(N)$ super Yang-Mills on
a squashed seven-sphere. We show that the localization locus of the partition
function has instanton membrane solutions wrapping the six "fixed"
three-spheres on the $\mathbb{S}^7$. The ADHM variables of these instantons are
fields living on the membrane world volume. We compute their contribution by
localizing the resulting three-dimensional supersymmetric field theory. In the
round-sphere limit the individual instanton contributions are singular, but the
singularities cancel when adding the contributions of all six three-spheres.
  The full partition function on the ${\mathbb S}^7$ is well-defined even when
the square of the effective Yang-Mills coupling is negative. We show for an
$SU(2)$ gauge theory in this regime that the bare negative tension of the
instanton membranes is canceled off by contributions from the instanton
partition function, indicating the existence of tensionless membranes. We
provide evidence that this phase is distinct from the usual weakly coupled
super Yang-Mills and, in fact, is gravitational.
