I would suggest you to do an RT-PCR using gene-specific primers. After that fractionate the amplicons on 1% agarose gel. if you got your desired sized bands, it means your cDNA construction was successful.
You can check by gel run and nano spec also, it's the easy and best method. Usually, 1.7 to 1.8 of 260/280 Value for cDNA is considered pure and can be used for PCR or qPCR.
use a small aliquot of your cDNA and PCR amplify GAPDH or beta-actin and if it amplifies...your cDNA is good. Be sure to add water only neg control to be sure
You can use a qubit to quantify your cDNA but if you know what you are looking for then you can also do an RT-PCR and target a gene of choice to check if it is present or not.