I'm going to assume you're not considering deep frying, which would generally be the easiest way to fry evenly on all sides (at once).
If you want something similar to pan frying, probably the simplest solution to get evenly browned cubes, assuming you have sufficient time, is to roast the food in the oven instead with a little oil or fat (which some people call "oven fried"). I'd particularly recommend this for "intermediate" sized cubes, which are too small and numerous to bother turning individually with tongs, but large enough that you care about all sides getting done.
Be sure the food is tossed well in your fat before putting in oven, space it out well in a single layer, and turn periodically. As long as you don't roast at a ridiculously high temperature, it's much harder to burn food this way, and the browning will be more even. It may take a little longer. But it's also lower maintenance, since you're less tempted to hover over the pan and can do other things without worrying about food burning.
If you have to do it in a pan (to achieve the texture you want or to do it faster), the most important thing is not to crowd the pan and have a single layer (but it sounds like you may already be doing that). The other general advice is to fry the first side the longest: it's always tempting to start turning early if you want to get it done fast, but it's important to get good color on the first side before starting the flipping. After the first toss, try your best to get most of the food with new sides down, and again wait a long enough time to get the second side cooked. After that, it's probably going to become much more difficult to always have a "new side" down, so decrease the time between subsequent tosses.
If you do the first two sides well, with small cubes this will often be enough to create the appearance of relative evenness (combined with the uneven later tosses). With larger cubes, you'll have to use tongs.
A few other factors may come into play which have to do with how easily and evenly the food will cook in general. For example, choose the right fat and the right pan temperature. If you're using only unclarified butter, the burning will start much earlier. It may be worthwhile either clarifying the butter and/or mixing butter with some fat that has a higher burning/smoke point (most oils, or bacon grease, etc.). Using an oil that is stable to higher temperatures will help to prevent burning. Pan type and surface can also play a role: a dark pan that food sticks to will burn more quickly, but it can also be helpful for cooking the first couple sides quickly, so it's a toss-up for quick cooking vs. higher maintenance.
Also, with some foods like potatoes, the way you prepare the cubes can make a difference in how easily they brown. For example, many recipes recommend blanching diced potatoes for a minute or so before cooking and then shocking with cold water before frying them in a preheated pan. This "precooking" will alter the starch characteristics on the exterior of the potatoes and make it easier to brown them faster (and more evenly).