Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?

There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.
Who are the following two guys?
A: B is a lying monkey. I am human.
B: A is telling the truth.

I have branches, but no fruit, trunk or leaves. What am I?

What comes
Once in a Year
Twice in a Month
4 times in a Week
6 times in a Day

Find the missing number in the sequence below:

On a charity event in Russia, Murray beat Djokovic by winning six games and losing three games.
Note: There is a total of 5 service breaks(one who serve lost the game).
Who served first, Djokovic or Murray?

Outside a massage parlour, there is a board that reads
"I only massage those who do not massage themselves."

Reading the above statement, does the masseur massage himself?

If you were to put a coin into an empty bottle and then insert a cork into the neck, how could you remove the coin without taking out the cork or breaking the bottle?

John said, "If yesterday was tomorrow, today would be Friday."

When did John make this statement?

A word I know has six letters it contains, remove one letter and 12 remain. What is it?