How much energy does cache memory consume in a modern processor?
I don't have a numerical answer but, you can get some idea from the following Intel presentation of Ivy Bridge.

First the photo of the die colored by functional areas:


The area to right of the (green) cores is the L3 cache (LLC = last level cache, in Intelspeak). Then here are the IREM (infrared emission, thus heat) photos of the die:


I suppose if you knew the (unpublished) temperature scale, then you could reverse engineer the relative power of the areas. There's a full video of the talk on youtube but it doesn't add much info for this particular question. One interesting tidbit is that the cores' power plane is gated, but the L3 cache is not, so when the die is almost entirely off, the L3 cache seems to use the most power.