We study Waring rank decompositions for cubic forms of rank
n
+
2
n+2
in
n
+
1
n+1
variables. In this setting, we prove that if a concise form has more than one non-redundant decomposition of length
n
+
2
n+2
, then all such decompositions share at least
n
−
3
n-3
elements, and the remaining elements lie in a special configuration. Following this result, we give a detailed description of the
(
n
+
2
)
(n+2)
-th Terracini locus of the third Veronese embedding of
n
n
-dimensional projective space.