Laminar flows over a cube and a cuboid (cube extended in the streamwise direction) are numerically investigated for the Reynolds numbers between 50 and 350. First, vortical structures behind a cube and lift characteristics are scrutinized in order to understand the variation in vortex shedding characteristics with respect to the Reynolds number. As the Reynolds number increases, the flow over a cube experiences the steady planar-symmetric, unsteady planar-symmetric, and unsteady asymmetric flows. Similar to the sphere wake, the planar-symmetric flow over a cube can be divided into two different regimes: single-frequency regime and multiple-frequency regime. The former has a single frequency due to regular shedding of vortices with the same strength in time, while the latter has multiple frequency components due to temporal variation in the strength of shed vortices. Second, the effect of the length-to-height ratio of the cuboid on the flow characteristics is investigated for the Reynolds number of 270, at which planar-symmetric vortex shedding takes place behind a cube. With the ratio smaller than one, the flow over the cuboid becomes unsteady asymmetric flow, whereas it becomes steady flow for the ratios greater than one. With increasing the ratio, the drag coefficient first decreases and then increases. This feature is related to the flow reattachment on the side faces of the cuboid.