Question 1: Calculate the cube of 3.

Answer: 27

Question 2: What is the cube of 5?

Answer: 125

Question 3: Identify which of the following numbers are perfect cubes: 64, 100, 125, 216.

Answer: ["64","125","216"]

Question 4: Construct a cube number that is greater than 50 but less than 200. Show your reasoning.

Answer: 125 (since 5^3=125, which lies between 50 and 200)

Question 5: Calculate 4^3 and explain whether it is a cube number.

Answer: 64; Yes, 64 is 4^3, a cube number.

Question 6: A number is a cube number if it can be written as n^3. Given the number 1000, determine if it is a cube number and justify your answer.

Answer: Yes, because 10^3=1000.

Question 7: Identify the mistake in the following statement: 'Since 64 is a perfect square, it must also be a cube.'

Answer: Not all perfect squares are perfect cubes; 64 is a perfect square but not a perfect cube.

Question 8: Given the sequence of numbers: 8, 27, 64, 125, identify the pattern and predict the next number.

Answer: 216 (since these are 2^3, 3^3, 4^3, 5^3, next is 6^3=216)

Question 9: A box is filled with cubes, each with edge length 3 units. If the total volume of cubes is 216 cubic units, how many cubes are there? Show your working.

Answer: Number of cubes = 216 / (3^3) = 216 / 27 = 8

Question 10: Identify the common mistake students might make when recognizing cube numbers and explain how to avoid it.

Answer: Confusing perfect squares with perfect cubes; ensure to check the number as n^3, not n^2.

Question 11: Challenge: Find all cube numbers between 1 and 1000 and list them.

Answer: [1, 8, 27, 64, 125, 216, 343, 512, 729, 1000]