  Spherical nucleus puzzle implies that the phonon excitation of a spherical
shape should be questioned and refuted. For understanding this spherical-like
$\gamma$-soft mode newly found experimentally, a possible answer was proposed
recently in the SU3-IBM. In this paper, the evolutions of the normal states in
$^{108-120}$Cd are investigated and compared with the experimental results. For
better explaining the nearly zero B(E2) values between the $0_{2}^{+}$ state
and the $2_{1}^{+}$ state, except for the SU(3) second-order and third-order
Casimir operators, other SU(3) higher-order interactions are also considered in
detail. It can be found that the results of theoretical fitting and
experimental data agree well under very simple parameter selection. The
spherical-like spectra really exist. The deficiency may come from the lack of
configuration mixing. The realistic spectra characteristics are found and it
predicts the electric quadrupole moment of the $2_{1}^{+}$ state for
$^{118,120}$Cd.
