Any string starting with 00,11,10,01 followed by either 0 or 1 is accepted.So the minimum length of the string which is accepted by this DFA is 3 and Regular Expression is of the form $(0+1)^{^{3}}$$(0+1)^{^{*}}$, so every string of length >=3 is accepted ,hence number of 8 length string that can be formed using {0,1} is $2^{^{8}}$ i.e 256, so all the string will be accepted i.e 256 string will be accepted.