In this work, we determine the general terms of balcobalancing numbers, balcobalancers and also Lucas-balcobalancing numbers in terms of balancing numbers. Further we formulate the sums of these numbers and derive some relations associated with Pell, Pell-Lucas and square triangular numbers.

"In this work, we derived some new algebraic results on continued fraction expansion of the ratio of the two consecutive balcobalancing numbers, circulant matrices and spectral norms, Pythagorean triples, characteristic polynomials and eigenvalues of the $n^{\text{th}}$ power of the companion matrices, Cassini and Catalan identities, cross-ratios and Heisenberg groups related to balcobalancing numbers, Lucas-balcobalancing numbers and balcobalancers."