  There are some dozen supernovae (SNe) associated with long Gamma-ray bursts
(GRBs) have been confirmed. Most of previous studies derive the physical
properties of the GRB-SNe by fitting the constructed (psuedo-)bolometric light
curves. However, many GRB-SNe have only a few filter data, for which the
(psuedo-)bolometric light curves are very difficult to be constructed.
Additionally, constructing (psuedo-)bolometric light curves rely on some
assumptions. In this paper, we use the multi-band broken power-law plus
$^{56}$Ni model to fit the multi-band light curves of the afterglows and the
SNe (SN~2001ke, SN~2013dx, and SN~2016jca) associated with three GRBs
(GRB~011121, GRB~130702A, and GRB~161219B). We find our model can account for
the multi-band light curves of the three GRB-SNe (except for the late-time
$z-$band light curves of two events), indicating that the model is a reliable
model. The $^{56}$Ni masses we derive are higher than that in the literature.
This might be due to the fact that the $^{56}$Ni masses in the literature are
usually obtained by fitting the psuedo-bolometric light curves whose
luminosities are usually (significantly) underestimated. We suggest that the
multi-band model can not only be used to fit the multi-band light curves of
GRB-SNe that have many filter observations, but also fit those having sparse
data.
