Reproduction
Gelatinous cubes, unsurprisingly, do not reproduce sexually. Some have tried to make gelatinous cubes mate with each other, but such efforts are doomed to failure. As they amoeboid life-forms, it is impossible to tell if a cube is male or female and futile to try. While cubes can sense motion and are drawn towards creatures that move, there is no evidence of a mating instinct at work. The gelatinous cubes simply slide towards each other and coalesce into a much larger gelatinous cube. Whether this the creatures form into a corporate entity or one simply absorbs and digests the other is unknown, and all attempts to approach the gelatinous cubes for answers have ended either in silence from the cube or in the questioner being engulfed and digested.
Gelatinous cubes reproduce by budding, leaving transparent rubbery cubes behind them as they slither along. The parent is unaware of its offspring, and is as likely to reabsorb it as ignore it.
Life-Cycle
Immature gelatinous cubes quickly grow to full size. This occurs in three stages.
The first stage begins with an endothermic reaction. The cube absorbs ambient heat from whatever sources are available, breaking down its structure into a semiliquid state. Its mass hardly changes during this phase and it retains the same general shape; however its size increases as the cube's insides 'melt' and its edges expand to accomodate the creature's liquid body. Over a 24-hour period the immature gelatinous cube grows to five feet in height, width and depth, beginning to resemble its parent more closely. This initial growth spurt enables the gelatinous cube to feed. The greater surface area ensures they absorb a greater amount of nutrients from walls, floors and ceilings; mosses, lichens, droppings, insects: it all adds up. If it's organic the gelatinous cube can eat it and continue to grow.
The second stage occurs soon after. During this period the gelatinous cube stabilises or 'jellifies'. As it eats, the gelatinous cube absorbs more solids and disperses them throughout its body, shifting its physical state into a gel. Once the cube has jellified it becomes truly mobile, and its third phase begins.
Now fully mobile, the gelatinous cube is able to seek out prey. The cube develops 'blindsense': it senses vibrations through the membranes that cover its six faces, and equates any movement it detects with food. The gelatinous cube also senses heat to a modest degree.
Throughout their lifespans, which are indeterminate, gelatinous cubes continue to grow. This rate of growth is limited only by the availability of food and the confines of its environment. If there is not sufficient space for the cube to grow, the gelatinous cube utilises a second form of asexual reproduction. The cube subdivides into two or more smaller gelatinous cubes, which either head in separate directions or attempt to absorb each other.
Mindset
The gelatinous cube has no brain and only rudimentary senses. It is mindless and cannot be reasoned with. All attempts to communicate with, train or control them are doomed to failure. The best that an owner of a gelatinous cube can hope to achieve is to guide its behavior; by reducing its scope for movement, a dungeon keeper can confine it to a smaller range of behaviours.