A note on the ranks of 2?×?2?×?2 and 2?×?2?×?2?×?2 tensors

Using rank-1 reduction formula and the vector space spanned by the real rank-1 matrices, we present a different way to show that the maximum possible rank of the 2?×?2?×?2 tensors over the real field is 3. Following, we obtain that the maximum rank of the 2?×?2?×?2?×?2 tensors over the real field is less than or equal to 5 and propose another way to show that the maximum rank of the 2?×?2?×?2?×?2 tensors over the complex field is 4, except one special case.