Evaluation of the convolution sums ∑l+6m=nσ(l)σ(m)∑l+6m=nσ(l)σ(m) and ∑2l+3m=nσ(l)σ(m)∑2l+3m=nσ(l)σ(m)

The sums ∑(l,m)∈N2,l+6m=nσ(l)σ(m)∑(l,m)∈N2,l+6m=nσ(l)σ(m) and ∑(l,m)∈N2,2l+3m=nσ(l)σ(m)∑(l,m)∈N2,2l+3m=nσ(l)σ(m) are evaluated for all n∈Nn∈N, and their evaluations used to determine the number of representations of a positive integer n by the formx12+x1x2+x22+x32+x3x4+x42+2(x52+x5x6+x62+x72+x7x8+x82).