Is there a number k such that every natural number can be written as $\sum\_{i=1}^k \binom{a\_i}{3}$ for some natural numbers $a\_i$'s?



Waring problem for binomial coefficients (generalization of Gauss' Eureka Theorem)
Watson's nice paper "Sums of eight values of a cubic polynomial" (<http://jlms.oxfordjournals.org/content/s1-27/2/217.full.pdf>) shows that we may take $k = 8$.


