Counting all cubes in {0,1,...,n}^3

TL;DR

This paper presents a method to count all cubes with vertices in the integer grid {0,1,...,n}^3, extending previous work on tetrahedra and expanding an integer sequence.

Contribution

It introduces a procedure for counting all such cubes, adapting existing code and theoretical results to extend the sequence A098928 to 100 terms.

Findings

Extended the sequence A098928 to 100 terms

Developed a counting procedure for all cubes in the grid

Built on previous tetrahedra counting methods

Abstract

In this paper we describe a procedure of calculating the number cubes that have coordinates in the set {0,1,...,n}. We adapt the code that appeared in [11] developed to calculate the number of regular tetrahedra with coordinates in the set {0,1,...,n}. The idea is based on the theoretical results obtained in [13]. We extend then the sequence A098928 in the Online Encyclopedia of Integer Sequences to the first one hundred terms.