How Radix-8 and Radix-2^3 are related How are Radix-8 and Radix-2^3 FFT are related?

Are they same?

I got some more details in IEEE paper by
S.He and M. Torkelson, "Designing pipeline FFT processor for OFDM (de)modulation," in Proc. Int. Symp. Signals, Syst., 1998, pp. 257-262.

FFT Radix 2^3 has complexity of radix 8 but has a structure as that of radix-2.
Radix-2^3 is a special class of radix-2 algorithms where the basic decomposition is based on radix-8 and the 8-point DFTs are later on decomposed into radix-2, leading to an algorithm based on radix-2 butterflies.

"Same" depends on what you mean and how you classify algorithms. In some sense, a valid way to implement a radix-8 butterfly is to decompose it into radix-2 butterflies. Still, using classic definitions, the size of the fundamental butterfly operation that is realized determines the radix, leading to that radix-8 and radix-2^3 are "different".