Multiscale entropy (MSE) has attracted many applications in revealing the complexity of bio-signals since its introduction in early 2000. To better understand the MSE method, a lot of researchers have been working on its analytical solution. The existing analytical solutions are limited either to bulky double integrals, or to a proportional relation. This study intends to solve the double integrals and further approximate the analytical formula of MSE. Combining Costa's method with Briggs' integral and Taylor series expansion, we approximated the analytical formula of MSE for uncorrelated (white) noise. With the additional help of the eigenvalue of a fractal Brownian motion process, we approximated the analytical formula of MSE for correlated noise (1/f noise). The analytical formulae were verified on simulated power noise with known scaling exponent. The proposed analytical solution may shed some light on the understanding of MSE in analyzing biological time series.