There are two.
Yes. In fact, they are integers.
The perfect cubes among the first 1000 natural numbers are the cubes of the integers from 1 to 10, since (10^3 = 1000). These integers are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. Therefore, there are 10 perfect cubes in the first 1000 natural numbers.
The perfect odd cubes between 1000 and 3000 are the cubes of odd integers that fall within this range. The smallest odd integer whose cube is greater than 1000 is 11 (since (11^3 = 1331)), and the largest odd integer whose cube is less than 3000 is 13 (since (13^3 = 2197)). Therefore, the perfect odd cubes between 1000 and 3000 are 1331 and 2197.
125,216,343,512
Perfect cubes between 1 and 1000 are the results of raising integers to the third power. The perfect cubes in this range are: 1 (1³), 8 (2³), 27 (3³), 64 (4³), 125 (5³), 216 (6³), 343 (7³), 512 (8³), and 729 (9³), and 1000 (10³). Thus, the perfect cubes from 1 to 1000 are: 1, 8, 27, 64, 125, 216, 343, 512, 729, and 1000.
26
Yes. In fact, they are integers.
The perfect cubes among the first 1000 natural numbers are the cubes of the integers from 1 to 10, since (10^3 = 1000). These integers are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. Therefore, there are 10 perfect cubes in the first 1000 natural numbers.
Infinitely many. However, if you meant perfect cubes between 0 and 150 (both inclusive), there are 6.
The perfect odd cubes between 1000 and 3000 are the cubes of odd integers that fall within this range. The smallest odd integer whose cube is greater than 1000 is 11 (since (11^3 = 1331)), and the largest odd integer whose cube is less than 3000 is 13 (since (13^3 = 2197)). Therefore, the perfect odd cubes between 1000 and 3000 are 1331 and 2197.
125,216,343,512
Perfect cubes between 1 and 1000 are the results of raising integers to the third power. The perfect cubes in this range are: 1 (1³), 8 (2³), 27 (3³), 64 (4³), 125 (5³), 216 (6³), 343 (7³), 512 (8³), and 729 (9³), and 1000 (10³). Thus, the perfect cubes from 1 to 1000 are: 1, 8, 27, 64, 125, 216, 343, 512, 729, and 1000.
100
The first six perfect cubes are 1, 8, 27, 64, 125, and 216. These correspond to the cubes of the integers 1 through 6, respectively: (1^3 = 1), (2^3 = 8), (3^3 = 27), (4^3 = 64), (5^3 = 125), and (6^3 = 216). Perfect cubes are numbers that can be expressed as the cube of an integer.
The perfect cubes between 1 and 25 are the numbers that can be expressed as (n^3) where (n) is a whole number. The perfect cubes in this range are 1 (from (1^3)), 8 (from (2^3)), and 27 (from (3^3)), but since 27 exceeds 25, we only consider 1 and 8. Therefore, the perfect cubes between 1 and 25 are 1 and 8.
The perfect cubes between 10 and 30 are 27, which is the cube of 3 (3^3). The next perfect cube, 64 (4^3), exceeds 30, while the perfect cubes below 10 are 1 (1^3) and 8 (2^3). Therefore, 27 is the only perfect cube in that range.
1, 8, 27