"The whole month?"
In the sense of "the entire/whole" or "all of", only hela is used, without an article, and followed by a definite form. Same with other similar words, such as halva 'half of' or båda 'both of'. (Note the sense of measuring/specifying with these words)
If you use it with an article you'll get the other sense of the word, 'whole' as in 'unbroken'.
Hela huset = The entire house
Det hela huset = The unbroken house
It is in English too, that's why it's called month. A month is approximately one moon-cycle, but it doesn't work out perfectly, which is why there can sometimes be two full moons in the same month. People were already using months to measure time in the Stone age, according to https://en.wikipedia.org/wiki/Month