The different wavelength can have two effects on the x-ray diffraction:
a) the more energetic radiation is more penetrating (lower wavelength), therefore an higher volume is interested to the diffraction and this increases all the intensities by an unique factor
b) the atomic form factors ( in your case of Cd and S) have a different behavior with respect the energy, therefore their relatives values depend from the wavelength of the x-rays. In such a case the variation of the peaks intensities are not changed by an unique factor, but vary for each diffraction angles.
The XRD Intensity from an 'infinitely-thick' powder pattern is indeed proportional to (1) wavelength-cubed and (2) inversely proportional to the linear attenuation coefficient which in turn also depends on the wavelength.
While the wavelength-cubed relationship is correctly stated above, the rationale in terms of the underlying physics is wrong - especially the formula quoted in the first answer is inappropriate.