Constructing 4-to-16 decoder using 3-to-8 decoders?

Sure, but some additional glue logic is needed. Place AND gates on the most significant bits of each decoder. On the decoder that will form the outputs for inputs 0 through 7 wire an inverter into the AND gate that will form the new most significant input. Connect the input to that inverter to one of the AND gate inputs on the other decoder - that will form input bit 3. Bit 2 will be the unconnected AND inputs connected together, and bits 0 and 1 on each decoder need wiring together and used as those inputs on the new decoder.