Summary: Let \(\mathbb F\) be a field of characteristic different from 2. It is shown that the problems of classifying
(i) local commutative associative algebras over \(\mathbb F\) with zero cube radical,
(ii) Lie algebras over \(\mathbb F\) with central commutator subalgebra of dimension 3, and
(iii) finite \(p\)-groups of exponent \(p\) with central commutator subgroup of order \(p^3\),
are hopeless since each of them contains
\(\bullet\) the problem of classifying symmetric bilinear mappings \(U\times U\to V\), or
\(\bullet\) the problem of classifying skew-symmetric bilinear mappings \(U\times U\to V\),
in which \(U\) and \(V\) are vector spaces over \(\mathbb F\) (consisting of \(p\) elements for \(p\)-groups, (iii)) and \(V\) is 3-dimensional. The latter two problems are hopeless since they are wild; i.e., each of them contains the problem of classifying pairs of matrices over \(\mathbb F\) up to similarity.