When asked about the ages of her three children, Mrs. Arithmetic replied to Mrs. Algebra in the following manner:

"The sum of the ages of my children is precisely 3 times that of Alec who is 3 years younger than Laura. The cube of Laura's age together with the square of Alec's age plus Karl's age make up a multiple of 100"

Determine the ages of the three children if Alec is still in his twenties.