If you want to avoid the simple and obvious solutions:
- place signs above the cubicles reminding people to be quiet
- encourage cubicle dwellers to discourage loud behavior through constant reminders ("Shh!" or "Please keep it down")
I suspect the only cultural design cues you could rely on are reverence (church, monastery) or respect (library, courtroom, bank). Though you may be able to change the lighting and get the desired effect as well.
As you don't indicate the type of business or the employee culture you have developed or are trying to develop (beyond a quiet culture) then it's hard to make suggestions.
First of all, though, spend time and money adding sound dampening to the office. The hard drywall cubicle walls you speak of are great reflectors, and spread sound around very easily. Consider adding heavy cloth to them. Replace ceiling tiles with more absorbent tiles. If you can't reduce total noise, you can at least prevent it from bouncing around so it stays very local. Encourage workers to add rugs to their cubicles, or bring stuffed toys. There are some fairly nice foam audio control products cut in attractive patterns that can be added throughout the space, particularly in the high traffic areas, that won't look out of place.
Second, choose the cultural cues that remind people of typically quiet places for their culture. For instance, in the US, having even a few rows of floor to ceiling bookshelves will suggest a place of quiet thought. Using gentle desk lamps in public areas suggestive of banking or libraries producing small pools of light rather than communal, harsh direct overhead lighting will encourage quiet behavior.
Rather than having long corridors through cubicles, embrace labyrinth or maze design patterns. These require thought to navigate, and distracted movement through them, such as during a phone call, won't produce good results. Forcing people to think about where they're at and where they are going will cause them to be more present in the space and aware of their surroundings. It will reduce rushing.
Also, and this may be cross-cultural, reducing overall lighting produces a very pronounced effect in human noise. When I worked in an engineering company many years ago, one design department had their overhead lights turned off (they actually just removed the bulbs from overhead fixtures except in certain areas of the floor), and each employee had desk lamps that fit their needs. Watching people move into and out of this space was dramatic - they immediately decreased their volume of ongoing conversation (phone or while walking with others) moving into the space, and increased it when moving out of it. I don't recall ever hearing anyone actively shush others - this seemed to be natural human behavior. This would require some investment in desk and task lamps, but may be overall cheaper and more effective than most other methods. It might even save you some electricity.