Besides the warming of the ocean, sea level is mainly rising due to land ice mass loss of the major ice sheets in Greenland, the West Antarctic, and the Alaskan Glaciers. However, it is not clear yet how these land ice mass losses influence regional sea level. Here, we use the global Finite Element Sea-ice Ocean Model (FESOM) to simulate sea surface height (SSH) changes caused by these ice mass losses and combine it with the passive ocean response to varying surface loading using the sea level equation. We prescribe rates of fresh water inflow, not only around Greenland, but also around the West Antarctic Ice Sheet and the mountain glaciers in Alaska with approximately present-day amplitudes of 200, 100, and 50 Gt/yr, respectively. Perturbations in sea level and in freshwater distribution with respect to a reference simulation are computed for each source separately and in their combination. The ocean mass change shows an almost globally uniform behavior. In the North Atlantic and Arctic Ocean, mass is redistributed toward coastal regions. Steric sea level change varies locally in the order of several centimeters on advective time- scales of decades. Steric effects to local sea level differ significantly in different coastal locations, e.g., at North American coastal regions the steric effects may have the same order of magnitude as the mass driven effect, whereas at the European coast, steric effects remain small during the simulation period.