Hi Ronnie, you purchased a 5 liter barrel with an outside coating of lacquer and if that barrel was properly hydrated you shouldn't lose any rum at all. In order for oxidation / evaporation some calling it Angels Share to take effect it needs to be an uncoated neutral barrel or one that no longer imparts much color and flavor and needs to be stored in the proper temperature and humidity like a cellar over a period of several months or years. An coated barrel that has only been used 30 days will not lose any rum at all, these new mini barrels impart so much color and flavor so quickly that the ingredients cannot be left inside long enough for oxidation to take place, there would be too much flavor from the oak, at least not until the barrel has been used several times, perhaps five years, and there isn't much color and flavor left. I say in my item description that “Smaller barrels provide each liter of spirits with a great deal more oak character than a larger barrel due to the ratio of surface area to wine volume. Because of this the same degree of flavor change may be observed in a far shorter period of time, perhaps only a few weeks. Spirits in a small barrel requires constant monitoring to ensure it does not become over oaked.”
In the Care and Storage Instructions emailed with the tracking number I describe one way a barrel might leak; “The hand carved wooden spigot / faucet / tap is shipped uninstalled to eliminate damage during shipping. The spigot is hand-made and the off position is not always exactly 90 degrees to the barrel, keep a cup under your spigot until you find the exact off position.” If you weren't monitoring your barrel you might have lost some rum dripping out of the spigot but you should have noticed a stain on the surface under the spigot. But even with a dripping spigot I don't believe you could lose 2.7 liters without noticing.
More than likely what happened is that someone was helping you monitor your rum. At your service Clay Johnston