  Let $E$ be a modular elliptic curve over a totally real cubic field. We have
a cubic-triple product motive over $\mathbb{Q}$ constructed from $E$ through
multiplicative induction; it is of rank $8$. We show that, under certain
assumptions on $E$, the non-vanishing of the central critical value of the
$L$-function attached to the motive implies that the dimension of the
associated Bloch-Kato Selmer group is $0$.
