Eagle and vias - board layout
Though @Samuel has already written what you need, here is a little more about the (EAGLE) internals.

PCBs are usually made of a resin reinforced by glass fibers. To make multi-layer PCBs, usually several thin double-layered PCBs (cores) are made and glued together by a so called prepeg. After this, the vias are drilled and the walls of the holes are coated by metal to make the vias conductive.

However, it's possible to add vias already to the cores and so to make vias between distinct layers. But this adds extra work / costs.

EAGLE allows to configure between which copper layers vias can be made in the LAYERS tab of the design rule window:



Here, two cores (green) are glued together by a prepeg (grey), and vias are possible through each core as well as the whole PCB. This is defined by the string ((1*2)+(15*16)) in the setup. 

You can change it to (1*2*15*16) which also defines a four-layer PCB, but only with vias across the whole board.

Finally, you can of course your set up and use "1-16" vias only, and this is more for completeness.