Any way to see "cubic-active" vibrational modes in molecules?
The product $xyz$ is an odd function and as such should produce the same selection rules as 1 photon (electric dipole) transitions. Thus CO has a 1 photon transition at 146.7 nm in the vacuum uv that can be more easily reached with a 3-photon transition with a pulsed laser at 440 nm. ( Three photon transitions are also used in bio-imaging where a ir photon is used so as not the excite the sample. Also, as the transition is multiphoton the focus area is smaller than a 1 photon transition and this improves spatial resolution).

As the product $xyz$ can be thought of as $xy$ multiplied by $yz$ then this is like a double Raman transition. Raman involves a change in polarisability. Polarisability is proportional to a volume but the projection for the radiation is 2D hence $xy$ type products in the point group tables. A  Raman type transition may occur between 4 levels. Levels 1 and 4 are  'real' and 2 and 3 'virtual'. The steps are 1 up to 3 , 3 down to 2, and 2 up to 4. This has been demonstrated in doppler free geometry between Na $3^2S_{1/2}\to 3^2P_{1/2}$.