We describe the first example of a primitive cubic lattice assembled spontaneously from three mutually orthogonal and intersecting arrays of cylindrical, multimode waveguides. The lattice is generated in a single, room-temperature step with separate (mutually incoherent) incandescent light bulbs. To demonstrate its potential as a nonlinear photonic lattice, we generated a self-trapped lattice beam of incoherent white light. These two findings open entirely new experimental opportunities to study the behavior of spatially and temporally incoherent, polychromatic lattice solitons in 3-D Bravais lattices.