# Your Task
You have a cuboid with dimensions x,y,z ∈ ℕ. A subcuboid of this cuboid has dimensions length, width, height ∈ ℕ where 1≤length≤x, 1≤width≤y, 1≤height≤z. If two subcuboids have the same length, width, and height, but they are at different positions within the cuboid, they are distinct. Find the total number of subcuboids for the given cuboid.
# Examples
See sample tests and the image below
### 27 subcuboids for a 2×2×2 cuboid
![subcuboids(2,2,2)](https://i.imgur.com/3CnboOW.jpg)

Source: codewars | Difficulty: EASY
Tags: Mathematics

Ad-hoc

Starter code: def subcuboids(x,y,z):
	

Solutions:
def subcuboids(x, y, z):
	return x * y * z * (x + 1) * (y + 1) * (z + 1) // 8


def n(x):
	return x * (x + 1) // 2

def subcuboids(x, y, z):
	return n(x) * n(y) * n(z)


subcuboids = lambda Q, W, E: Q * -~Q * W * -~W * E * -~E >> 3


subcuboids = lambda x, y, z: x * -~x * y * -~y * z * -~z / 8


def subcuboids(x, y, z):
	l = x * (x + 1) // 2
	m = y * (y + 1) // 2
	n = z * (z + 1) // 2
	return int(l * m * n)


def subcuboids(x, y, z):
	if x * y * z % 2 == 0:
		return (x + x ** 2) // 2 * ((y + y ** 2) // 2) * ((z + z ** 2) // 2)
	else:
		return x * y * z * ((x - ((1 + x) // 2 - 1)) * (y - ((1 + y) // 2 - 1)) * (z - ((1 + z) // 2 - 1)))