From Google Earth I can see a strange, very white, square object
located in the central region of Antarctica.  Here are the
coordinates:  -81.417276 Lat, 106.945272 Lon.  It appears to be
approximately a mile on each side (the resolution of the photo is
rather low compared with other locations visible from Google Earth).

What is it?  Simply a "flare" or a bad pixel in the orbital camer?  Or
is there some kind interesting geological phenomenon?

Your citing of the co-ordinates do not specify south for the 81
degrees. But because it is Antarctica, it is south.  Or east or west
of the Greenwich line [ 179 deg. east/ 179 deg.west]. The co-ordinates
of Google earth do give the south/north and east/west indicators. Also
non-use of the terms latitude and longitude do indicate a lack of
experience with navigation. In searching Google earth on the
co-ordinates given, I did find a large darkish mass but irregular, but
no square white object. But I will keep looking.

Sorry, you did use lat. and lon. apologies. But east or west?