The atomistic origin underlying the lower critical solution temperature (LCST) behavior of thermoresponsive copolymers in water is still elusive. Here, we report all-atom molecular dynamics simulations of block copolymers of 2-(2-methoxyethoxy)ethyl methacrylate (MEO(2)MA) and oligo(ethylene glycol) methyl ether methacrylate (OEGMA(300)) in water at various block ratios and at temperatures below and above the LCST values of each homopolymer block. Our single chain simulations showed that hydration water molecules accumulate particularly near the side chain carbon atoms by forming ordered cage-like structures via extensive hydrogen bonding between them. These water cage formations surround the entire surface of PMEO(2)MA-b-POEGMA(300) and enable the copolymer to remain in water below the LCST. As the temperature increases, each block exhibits a separate coil-to-globule transition above its own LCST. A detailed analysis of the interactions between polymer-water and water-water revealed that this phase transition is mainly driven by the reduced local water ordering by the disruption of the water cages when the temperature is increased above the LCST. We found that the transition occurs differently in the copolymer than the POEGMA homopolymers due to the interaction of the blocks, especially around the joint of the blocks. Accordingly, the phase transition of a block acts as an additional disruptive effect on the other block's water cage structure, which reduces the LCST values of PMEO(2)MA and POEGMA(300) in the copolymer, compared to their individual single chain homopolymers.