No, you can't extrude into a curve like that. Your best bet would be to take the single side that you have successfuly extruded, make it a group, then get rid of everything else. You then need to duplicate that group around all the other sides of the cube...even though the extrusions will overlap. Then, explode all those groups, select all the geometry and from the r-click menu, intersect it with itself. You are then faced with a lovely little clean-up job, deleting all the faces you don't want.