A train of few-laser-cycle relativistically intense radiation spikes with a terahertz repetition rate can be organized self-consistently in plasma from two frequency detuned co-propagating laser beams of low intensity. Large frequency bandwidth for the compression of spikes is produced via laser-induced periodic modulation of the plasma refractive index. The beat-wave-driven electron plasma wave downshifted from the plasma frequency creates a moving index grating thus inducing a periodic phase modulation of the driving laser (in spectral terms, electromagnetic cascading). The group velocity dispersion compresses the chirped laser beat notes to a few-cycle duration and relativistic intensity either concurrently in the same, or sequentially in different plasmas. Particle-in-cell simulations indicate that the effect persists in a realistic three-dimensional axisymmetric geometry.