Both bash and zsh have a way to perform indirect expansion, but they use different syntax.
It's easy enough to perform indirect expansion using eval; this works in all POSIX and most Bourne shells. Take care to quote properly in case the value contains characters that have a special meaning in the shell.
eval "value=\"\${$VAR}\"" echo "$VAR" echo '$value""$value" ${${VAR}} doesn't work because it's not a feature that any shell implements. The thing inside the braces must conform to syntax rules which do not include ${VAR}. (In zsh, this is supported syntax, but does something different: nested substitutions perform successive transformations on the same value; ${${VAR}} is equivalent to $VAR since this performs the identity transformation twice on the value.)