We construct explicit analytic solutions of the $SU(N)$-Skyrme model (for generic $N$) suitable to describe different phases nuclear pasta at finite volume in $(3+1)$ dimensions. The first type are crystals Baryonic tubes (nuclear spaghetti) while second smooth layers lasagna). Both, ansatz for spaghetti and lasagna phases, reduce complete set Skyrme field equations just one integrable equation...