Write the following program in C++ programming language.

1) Take in a single number. It will initialize an array named, "numbers". Print an error message if the number value is zero or negative. The number will be named, "N". The array should be size of "N+1".

2) Start at "0". Go through "N". This program should calculate a cumulative sum of the squares of numbers "0" to "N". Partial results at each stage will be stored within the array, "numbers", in order from left to right, starting at "0".