Recently, two-dimensional (2D) nonlinear instabilities of whistler waves from resonant wave-wave interaction have gained much attention in numerical simulations as well as observations in space plasmas. In this paper, both 2D and three-dimensional (3D) nonlinear instabilities of whistler waves are investigated using electron magnetohydrodynamics (EMHD). It is found that decay instabilities can excite waves with a broadband wavenumber spectrum, including highly oblique propagating whistler waves. Whistler waves with lambda(e)k = 1 would excite counter-propagating whistler waves, and the wave with lambda(e)k not equal 1 can produce both co- and counter-propagating whistler waves, where lambda(e) is the electron inertial length and k is the wavenumber. Moreover, it is shown that 3D instabilities have similar nonlinear growth rate distributions as in 2D decay for the azimuthal wavelength much larger than lambda(e). These results suggest that nonlinear wave-wave interaction can play an important role in the scattering of whistler waves in the solar wind and the Earth's magnetosphere, and are also helpful for understanding nonlinear wave-wave interaction in the formation and development of EMHD turbulence.