  We study the stochastic colored six vertex (SC6V) model and its fusion. Our
main result is an integral expression for natural observables of this model --
joint q-moments of height functions. This generalises a recent result of
Borodin-Wheeler. The key technical ingredient is a new relation of height
functions of SC6V model in neighboring points. This relation is of independent
interest; we refer to it as a local relation. As applications, we give a new
proof of certain symmetries of height functions of SC6V model recently
established by Borodin-Gorin-Wheeler and Galashin, and new formulas for joint
moments of delayed partition functions of Beta polymer.
