Only the second one is right. Remember that 'December', with its capital letter, is actually a name. You can't say the 'the whole December', just as you can't say 'the whole Alberto' or 'the whole Spain'. 'The whole...' can only work with common nouns, such as 'the whole body', 'the whole class' or 'the whole country.' Another alternative with names is to use 'all of'. You can say 'all of Spain' and 'all of December.'