  In the strong interaction limit, attractive fermions with $N$-component
hyperfine states in a one-dimensional waveguide form unbreakable bound cluster
states. We demonstrate that the ground state of strongly attractive SU($N$)
Fermi gases can be effectively described by a super Tonks-Girardeau gas-like
state composed of bosonic cluster states with strongly attractive
cluster-cluster interaction for even $N$, and a Fermi duality of a super
Tonks-Girardeau gas-like state composed of fermionic cluster states with weakly
interacting cluster-cluster p-wave interaction for odd $N$.
