A wheel and a rim with weight reduction sockets are provided. The rim includes an inner flange, a middle portion and an outer flange, the inner flange, middle portion and outer flange are all annular and are connected end to end to form a cylindrical rim, in which the middle portion of the rim includes weight reduction sockets; and the weight reduction sockets are of regular hexagons, and are arranged adjacently on the outer side of the middle portion of the rim in the shape of a honeycomb. The weight of the hub is reduced by designing the weight reduction sockets in a specific shape for the outer rim of the hub and selecting the size of the weight reduction sockets.