The analysis performed shows that in cubic photorefractive crystals (of Bi12SiO20 and GaAs type in particular) with drift (''quasilocal'') mechanism of optical nonlinearity spatial soliton propagation can be observed for reasonable external de electric fields 10-15 kV/cm. These photorefractive solitons which can be excited at very low cw laser power are stable in a broad region of signal(soliton)/incoherent(spatially uniform) intensity ratio, and allow easy switching from bright to dark type. Original experimental results of self-channeling of submicrowatt HeNe laser beam in a cubic Bi12TiO20 Sample under external de field are presented.