As LED installer Torchlight mentions, old dimmers are made to work with high-wattage incandescent bulbs. They don't really know what to do with low-wattage LEDs, which leads to burnout issues.
For a different approach to LED cubes, checkout this sweet panel based approach, and here’s a really small 4x4x4 module for those with less space to spare.
Field-Configurable Performance: PAXT LED Wall Pack offers selectable wattage options (10w, 15w, and 20w) and Kelvin temperature settings (3000K, 4000K, and 5000K), empowering users to tailor light ...
IKEA has launched its JETSTRÖM LED wall light panel in Europe. Unlike a lot of IKEA's other smart lights, the wall light can produce white light as well as coloured light. It will set you back £ ...