We report detection of PSR B0656$+$14 with the Gran Telescopio Canarias in narrow optical $F657$, $F754$, $F802$, and $F902$ and near-infrared $JHK_s$ bands. The pulsar detection in the $K_s$ band extends its spectrum to 2.2 $mu$m and confirms its flux increase towards the infrared. We also present a thorough analysis of the optical spectrum obtained by us with the VLT. For a consistency check, we revised the pulsar near-infrared and narrow-band photometry obtained with the textit{HST}. We find no narrow spectral lines in the optical spectrum. We compile available near-infrared-optical-UV and archival 0.3-20keV X-ray data and perform a self-consistent analysis of the rotation phase-integrated spectrum of the pulsar using unified spectral models. The spectrum is best fitted by the four-component model including two blackbodies, describing the thermal emission from the neutron star surface and its hot polar cap, the broken power-law, originating from the pulsar magnetosphere, and an absorption line near $sim$0.5 keV detected previously. The fit provides better constraints on the model parameters than using only a single spectral domain. The derived surface temperature is $T_{NS}^{infty}=7.9(3)times10^5$K. The intrinsic radius (7.8-9.9 km) of the emitting region is smaller than a typical neutron star radius (13km) and suggests a nonuniform temperature distribution over the star surface. In contrast, the derived radius of the hot polar cap is about twice as large as the `canonical one. The spectrum of the nonthermal emission steepens from the optical to X-rays and has a break near 0.1 keV. The X-ray data suggest the presence of another absorption line near 0.3keV.
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